A Mechanistic and Kinetic Study on the Decomposition of Morpholine

Jun 29, 2012 - ABSTRACT: The combustion chemistry of morpholine. (C4H8ONH) has been experimentally investigated recently as a representative model ...
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A Mechanistic and Kinetic Study on the Decomposition of Morpholine Mohammednoor Altarawneh*,† and Bogdan Z. Dlugogorski Priority Research Centre for Energy, Faculty of Engineering & Built Environment, The University of Newcastle, Callaghan NSW 2308, Australia S Supporting Information *

ABSTRACT: The combustion chemistry of morpholine (C4H8ONH) has been experimentally investigated recently as a representative model compound for O- and N-containing structural entities in biomass. Detailed profiles of species indicate the self-breakdown reactions prevailing over oxidative decomposition reactions. In this study, we derive thermodynamic and kinetic properties pertinent to all plausible reactions involved in the self-decomposition of morpholine and its derived morphyl radicals as a crucial task in the development of comprehensive combustion mechanism. Potential energy surfaces have been mapped out for the decomposition of morpholine and the three morphyl radicals. RRKM-based calculations predict the self-decomposition of morpholine to be dominated by 1,3-intramolecular hydrogen shift into the NH group at all temperatures and pressures. Self-decomposition of morpholine is shown to provide pathways for the formation of the experimentally detected products such as ethenol and ethenamine. Energetic requirements of all self-decomposition of morphyl radicals are predicted to be of modest values (i.e., 20−40 kcal/mol) which in turn support the occurrence of breaking-down reactions into two-heavy-atom species and the generation of doubly unsaturated four-heavy-atom segments. Calculated thermochemical parameters (in terms of standard enthalpies of formation, standard entropies, and heat capacities) and kinetic parameters (in terms of reaction rate constants at a high pressure limit) should be instrumental in building a robust kinetic model for the oxidation of morpholine.

1. INTRODUCTION Thermal treatment of biomass such as wood and agricultural straw has emerged as an important source of renewable energy. However, it results in the emission of nitrogen oxides, collectively termed as NOx, in addition to other toxic gases such as hydrogen cyanide (HCN) and ammonia (NH3).1 These compounds are sourced from the nitrogen-bound constituents in biomass including lignin and cellulose.2 In order to minimize the emission of these compounds to the environment, and their presence in food chain and water resources, it is essential to develop a detailed understanding of the chemical phenomena and reactions that govern their formation. Experimental studies on coal firing reveal that nitrogen content in coal is readily transformed into HCN, NH3, and NOx. It is widely accepted that nitrogen content in coal and biomass follows different mechanistic pathways and forms distinct products during thermal treatment. In fact, most nitrogen in biomass exists mainly in the form of amino acids, while in coal nitrogen is embedded in cyclic structural blocks.3 Thus, experimental and theoretical modeling in literature pertinent to the behavior of nitrogen during the combustion of coal cannot be extended to that of biomass. Knowledge of nitrogen chemistry in biomass is instrumental in the effort to improve practical combustion systems toward a zero-NOx emission level. Efforts to reveal how NOx is formed during firing © 2012 American Chemical Society

of biomass are hindered by the intricacy in the intrinsic properties of biomass, in particular by the presence of numerous structural entities that contain bound nitrogen.4 The presence of a significant amount of oxygenated species during the combustion of biomass also contributes to this complexity. Comprehension of the transformations and pathways of nitrogen in biomass is rather obscure. This is primarily due to the limited literature knowledge of thermodynamics, reaction pathways, and representative model compounds. To overcome the difficulty arising from the complex intrinsic properties of fuels in terms of their numerous complex structural entities, fuels are often represented by groups of model compounds or surrogates that have potential to mimic the burning behavior and the emission characteristics of the real materials. Recently, there has been a great deal of research on constructing fuel surrogates for various types of fuels such as gasoline, diesel, and jet fuel.5 Corresponding focus on biomass has targeted studying the most common structural blocks, i.e., alcohol, ethers, and esters.6 Addressing the potential emission of biomass-derived Received: April 11, 2012 Revised: June 29, 2012 Published: June 29, 2012 7703

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Moments of inertia of the rotors were calculated by using the Multiwell suite of programs.20 Pressure-dependent reaction rate constants are obtained by applying RRKM21 theory (Master equation) as implemented in the ChemRate code. The collisional energy transfer is described by using an exponential-down model with ΔEdown = 800 cm−1. This value is chosen to mimic intermediate collisions induced by the deployment of He as the bath gas.22 Lennard-Jones parameters for morpholine and its direct products are adopted from the corresponding values of pyrazine (C4H4N2), σ = 5.350 Å and k/εb = 307.0 K.23 Plausible contribution from quantum tunnelling on the rate constants is accounted for by incorporating tunnelling factors, based on Eckart’s formula,24 as implemented in the ChemRate code. This procedure requires evaluating separately barrier widths for all reactions as explained by Chandra and Rao.25 A sample calculation on the estimation of barrier width is given in the Supporting Information (SI).

fuels necessitates the consideration of heteroelements containing compounds, especially nitrogen and sulfur. In this regard, denitrogenation of fuel is typically more complex than desulfurization.7 Combustion and pyrolysis of several nitrogencontaining compounds were investigated recently with the aim of exploring the nitrogen conversion in biomass and coal, especially into NOx, NH3, and HCN. The selected model compounds include pyrrole,8 nitro-methane,9 pyridine,10 and leucine.11 In two recent studies, Lucassen et al.12 and Lucassen et al.13 investigated the combustion chemistry of morpholine as a model for oxygenated nitrogen-containing compounds present in the real biomass fuel. They have utilized the technique of mass beam time-of-flight mass spectrometry with tunable photoionization to obtain comprehensive species profiles including stable molecules and transient radicals. Lucassen et al.12 proposed several reaction pathways to account for the formation of major experimental products and intermediates. Despite the prevailing oxidative conditions, Lucassen et al.12 described that product profiles could be accounted for based on unimolecular decomposition of morpholine and its directly derived morphyl radicals. The latter are formed by hydrogen abstraction reactions from the parent morpholine. This process is carried out by diffusion of H atoms from the hot regions of the flame down toward the burner, where they readily react with the incoming fuel to produce morphyl radicals. The authors postulated that unimolecular reactions leading to smaller species could compete with oxidation reactions that commonly prevail for hydrocarbons. Thus, a detailed mechanism of the pyrolysis of morpholine could be instrumental to understand its decomposition under oxidative and pyrolytic operating conditions alike. In this study, a density functional theory approach coupled with accurate ab initio calculations is deployed to investigate reaction mechanisms that were postulated to be of profound significance during the thermal oxidative decomposition of morpholine. Thermochemical and kinetics information provided by this study will be instrumental in unravelling more insightful pictures of the decomposition behavior of nitrogen-bound species in biomass.

3. RESULTS AND DISCUSSION 3.1. Structure and Thermochemistry of Morpholine. Morpholine (C4H8ONH) is found to exhibit two geometries depending on the orientation of the H atom bound to the N atom with respect to the C4NO ring; namely, syn- and anti-conformers. The two conformers of morpholine are shown in Figure 1. In the

2. COMPUTATIONAL DETAILS The Gaussian0314 suite of programs was used to perform all structural and energy calculations with the G3MP2B315 composite method. The G3MP2B3 method carries out initial optimization and frequency computations at the B3LYP16/ 6-31G(d)17 level of theory followed by successive single point energy calculations at the QCISD(T,FrzG3) and MP2(FrzG3/ GTMP2Large) levels of theory. Intrinsic reaction coordinates (IRC) calculations were used to link transition structures with their corresponding reactants and products. Using unrestricted procedure, open shell singlet structures such as the biradical species were converged to an expected value for spin contamination of S2 = 0.00. Stability testing for wave functions of biradical species were performed with reoptimization and mixing for frontier orbitals. The ChemRate code18 was applied to derive thermochemical (entropies and heat capacities) and kinetics parameters (reaction rates). Internal rotations in products, intermediates, and transition structures were treated as hindered rotors. This treatment was shown to have a significant influence on deriving accurate thermochemical and kinetics parameters.19 Rotor potentials were obtained by scanning corresponding dihedral angles at an interval of 30° at the theoretical level of B3LYP/6-311+G(d,p).

Figure 1. Optimized structures of the two conformers of morpholine and their energetics. Bond lengths are in Å.

syn-conformer, the H atom lies in the same plane as the C4NO ring, whereas in the anti-conformer the H atom deviates from the planar C4NO ring at an angle of 69.35°. These two conformers are found to have very comparable stability, with the synconformer more stable than its anticonformer by only 0.8 kcal/ mol at 298.15 K. An enthalpic barrier for the conversion of synmorpholine into anti-morpholine is calculated to be 5.2 kcal/ mol. Accordingly, equilibrium is most likely to be established between these two conformers at high temperatures. In order to set a benchmark for the accuracy of the adapted methodology, the standard enthalpy of formation (ΔfH°298) of morpholine and its ring strain energy are calculated and compared with the corresponding experimental values. 7704

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Figure 2. Potential energy surface for the initial decomposition of morpholine. Values in bold are reaction enthalpies and values in italic are activation enthalpies. All values (in kcal/mol) are relative to the parent morpholine calculated at 298.15 K.

ΔfH°298 for morpholine is calculated based on the two isodesmic reactions R1 and R2:

Ring strain energy has been a subject of interest, especially for homocyclic structures.32 The hyperhomo desmotic reaction R3 is used to estimate the ring strain energy for morpholine:

Hyperhomo desmotic reactions32 conserve bonding environment around adjacent atoms in reactions and products. The calculated ring strain energy (ΔrH°298 for reaction R3) is found to amount to 2.9 kcal/mol, in excellent agreement with the corresponding experimental value of 3.0 kcal/mol.33 The agreement between calculated and experimental values of ΔfH°298 and ring strain energy demonstrates the accuracy of the adopted methodology of G3MP2B3 in describing the selfdecomposition of morpholine. 3.2. Potential Energy Surface for the Decomposition of Morpholine. Potential energy surface (PES) for the initial decomposition of morpholine is depicted in Figure 2. All values are based on relative enthalpies at 298.15 K. Initial decomposition of morpholine is found to afford eight distinctive pathways. The first three pathways are characterized by direct expulsions of H atoms and the generation of the three morphyl radicals, m-morphyl (M1), o-morphyl (M2), and p-morphyl (M3):

Reaction R1 utilizes the experimental enthalpies of piperidine (−11.27 ± 0.15 kcal/mol),26 tetrahydropyran (−53.5 ± 0.15 kcal/mol),27 and cyclohexane (−29.78 ± 0.20 kcal/mol).28 Reaction R2 deploys the experimental enthalpies of aziridine (30.20 ± 0.20 kcal/mol)29 and oxirane (−12.58 ± 0.15 kcal/ mol).27 Reactions R1 and R2 are associated with standard enthalpies of reactions of 0.7 kcal/mol and −52.9 kcal/mol, respectively. The uncertainty limit for each isodesmic reaction (uj) is estimated as (∑ui2)1/2in which ui represents the uncertainty pertinent to the experimental ΔfH°298 of the reference species. Calculated ΔfH°298 for morpholine from reactions R1 and R2 is found to amount to −34.0 ± 0.19 and −35.2 ± 0.25 kcal/mol, respectively. Thus, reactions R1 and R2 provide ΔfH°298 of −34.60 ± 1.18 kcal/mol at the 95% level of confidence. The final enthalpy and overall uncertainty values are estimated based on the approach developed by Simmie et al.30 In this procedure, the overall uncertainty is reported as 1/[∑(1/uj2)]1/2 and the final enthalpy is calculated via a weighted grand mean calculated as ∑(xj/uj2)/∑(1/uj2), where xj signifies ΔfH°298 from each isodesmic reaction. Final enthalpy is calculated to be −34.44 kcal/mol with an uncertainty value of 0.15 kcal/mol (i.e., −34.44 ± 0.15 kcal/mol). This value is in very good agreement with the experimental measurement of −34.30 kcal/mol.31

Formation of these three radicals is found to be endoergic by 93.2, 97.2, and 94.8 kcal/mol, respectively. 1,3-Hydrogen shift opens up decomposition pathways toward the formation 7705

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corresponds to the internal rotation of a CH2 group and not to the bond breakage. In an analogy to cycloalkanes,33−36 the fate of the three singlet biradical species is most likely to be controlled by further β-C−C bond scission or isomerization into more stable closed-shell structures. Despite numerous attempts to find transition structures for hydrogen molecule elimination from morpholine and formation of structures such as 2-(vinylamino)acetaldehyde and 2-(vinyloxy)ethanamine, we were unsuccessful:

of M4 (2-(vinylamino)ethanol) and M5 (2-(vinyloxy)ethanamine) intermediates. Formation of M4 and M5 is found to be slightly endothermic by 5.2 and 12.3 kcal/mol, respectively. 1,3-Hydrogen shifts leading to M4 and M5 take place via transition structures TS1 and TS2 with enthalpic barriers of 71.3 and 78.1 kcal/mol, respectively. Formation of M5 constitutes the most favorable exit channel in the initial decomposition of morpholine:

Geometries for all transition structures and optimized structures are given in Figures S1 and S2 of the Supporting Information, respectively. As shown in Figure 2, further decomposition of M4 occurs through 1,3-hydrogen transfer into the NH group and the subsequent generation of ethenol and ethenamine. Both ethenol and ethenamine are detected experimentally from the oxidation of morpholine, yet the model of Lucassen et al. does not predict their formation.12,13 Activation enthalpy of this process amounts to 74.3 kcal/mol via the transition structure TS4. Likewise, 1,3hydrogen shift in M5 forms ammonia and vinyloxyethene (CH2CHOCHCH2) climbing an enthalpic barrier of 65.0 kcal/ mol as characterized by the transition structure TS3. Vinyloxyethene was not reported to be a product,12,13 however, its isomer, methyl vinyl ketone (CH2CHCOCH3), which shares the same mass to charge ratio (m/z) with vinyloxyethene, was detected.13 To distinguish between these two isomers, we calculated their ionization energies (IE). Calculated IE values for vinyloxyethene and methyl vinyl ketone are found to amount to 8.33 and 9.45 eV, respectively. The calculated IE value for methyl vinyl ketone matches the corresponding observed (9.7 eV) and literature (9.65 eV) IE values for methyl vinyl ketone. It follows that the detected isomer with (m/z 70) is most likely to be methyl vinyl ketone. The detected methyl vinyl ketone (and its derived vinylmethoxy radical (•CH2OCHCH2)) could be sourced from the bimolecular reaction C2H3 + CH2O as suggested.12 In their proposed mechanism, Lucassen et al.12,13 explained that all experimentally detected products are generated from the decomposition of the three morphyl radicals. PES in Figure 2 shows that decomposition of morpholine itself forms some of the experimental products in alternative pathways to those that pass through morphyl radicals. As an important process in the decomposition of cycloalkanes, the ring-opening has been studied extensively, both experimentally and theoretically.34−36 Herein, we investigate the three possible structures that could result from ring-opening of morpholine. Formation of the three singlet biradical species of M6 (β-H2C−NH scission), M7 (β-H2C−O scission), and M8 (β-H2C−CH2 bond scission) is found to be endothermic by 76.6, 102.6, and 85.1 kcal/mol, respectively. Scanning the corresponding elongated bond confirms the nonexistence of genuine transition structures for the three biradicals. Sirjean et al.37 found a transition structure for ringopening in cyclohexane. However, reoptimizing this transition structure, using the authors’ theoretical method (CBS-QB3) and its Cartesian coordinates provided in their Supporting Information, reveals that this transition structure actually

3.3. Potential Energy Surface for the Decomposition of the Three Morphyl Radicals. While the initial decomposition of morpholine is most likely to commence through intramolecular hydrogen shift or β-C−C bond scission rather than through direct H elimination, morphyl radicals could readily be formed through reactions with the H/O radical pool. As the bond dissociation enthalpies for the three radicals (M1, M2, and M3) are within 4.0 kcal/mol, it is expected that the three morphyl radicals could contribute to the flux of products. In this section, we investigate the mechanisms proposed by Lucassen et al.12,13 to account for the product profiles. Key steps in this mechanism correspond to breaking down reactions into two-heavy-atom species and the generation of doubly unsaturated four-heavyatom segments. Figures 3, 4, and 5 show PES for the unimolecular decomposition of the three morphyl radicals, M2, M1, and M3, respectively. As shown in Figure 3, decomposition of M2 commences either via β-H2C−NH or β-H2C−O bond scission. These two reactions are characterized by comparable activation enthalpies of 29.4 (TS5) and 24.1 kcal/mol (TS6), respectively. Products are M10 and M17 intermediates with reaction enthalpies of 5.5 and 13.3 kcal/mol, respectively. The fate of M10 and M17 intermediates is characterized by either H eliminations or departures of two-heavy-atom molecules. H elimination from M10 and M17 is calculated to be endothermic by 25.1 and 28.5 kcal/mol, respectively, and results in the formation of the two C4H7NO isomers of M11 (2-(vinylamino)acetaldehyde) and M9 (2-(vinyloxy)ethanimine). Ethene and methyleneimine molecules along with the two four-heavy-atom adducts of M12 and M18 are sourced from M10 and M17 moieties with enthalpic barriers of 21.0 and 20.9 kcal/mol, respectively. These two reactions are endothermic by 16.4 and 16.7 kcal/mol, respectively. Further decomposition into (H2CNH + HCO) occurs without encountering a reaction barrier with a trivial endothermicity of 8.2 kcal/mol. M18 moiety dissociates to C2H3 and H2CO with a barrier of 37.3 kcal/mol (TS9) and endothermicity of 23.1 kcal/mol. In view of the noticeable difference in the enthalpic barriers between TS10 and TS13, i.e., 30.5 kcal/mol, decomposition of M1 is most likely to proceed via a β-H2C−NH bond scission 7706

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Figure 3. Potential energy surface for the decomposition of the radical m-morphyl (M2) radical. Values in bold are reaction enthalpies and values in italic are activation enthalpies. All values (in kcal/mol) are relative to the parent reactant (M2) calculated at 298.15 K.

Figure 4. Potential energy surface for the decomposition of the radical o-morphyl (M1) radical. Values in bold are reaction enthalpies and values in italic are activation enthalpies. All values (in kcal/mol) are relative to the parent reactant (M1) calculated at 298.15 K.

Figure 5. Potential energy surface for the decomposition of the radical p-morphyl (M3) radical. Values in bold are reaction enthalpies and values in italic are activation enthalpies. All values (in kcal/mol) are relative to the parent reactant (M3) calculated at 298.15 K.

19.3 kcal/mol through the transition structure TS16, which resembles a β-H2C−C2H bond scission, into the intermediate M19. Further decomposition of M20 produces (C2H4 + H2CO + NCH2) in an energetic trend similar to that found for the

affording the intermediate M13. As shown in Figure 4, M13 could dissociate into (C2H4 + H2CO + NCH2) through a twostep process or yield the structure M9 via direct H elimination. As given in Figure 5, M3 decomposes via an activation enthalpy of 7707

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Table 1. Thermochemical Parameters. ΔfH°298 Values (in kcal/mol) and Values of S°298 and Cp°(T) (in cal/mol·K)a Cp°(T) morpholine M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 M13 M14 M15 M16 M17 M18 M19 M20 TS1 TS2 TS3 TS4 TS5 TS6 TS7 TS8 TS9 TS10 TS11 TS12 TS13 TS14 TS15 TS16

ΔfH°298

S°298

300 K

500 K

750 K

1000 K

1250 K

1500 K

−34.0 7.0 11.0 9.4 −28.8 −21.7 42.6 68.0 47.1 0.7 16.5 −10.5 20.4 25.6 28.0 26.0 55.2 24.3 24.8 28.0 63.4 44.1 37.3 43.3 45.5 40.2 35.1 43.4 37.5 62.1 36.0 48.0 38.5 66.2 28.5 98.6 28.7

75.78 76.37 76.40 76.06 85.43 87.56 86.33 84.41 86.91 86.98 87.56 84.99 73.41 88.00 72.48 85.12 72.53 86.97 72.55 87.67 73.63 77.45 80.55 88.07 85.17 80.32 77.84 88.54 89.16 81.34 79.83 90.85 74.38 81.17 87.89 78.65 77.10

23.38 23.78 23.63 23.12 27.96 28.40 29.38 27.82 30.37 27.18 28.91 26.20 19.14 28.51 18.31 27.52 20.78 27.93 19.26 28.48 20.01 25.40 26.96 28.19 28.40 25.59 24.64 28.31 29.00 20.27 26.32 28.76 17.91 26.19 28.24 20.77 24.10

39.13 38.26 38.18 37.83 42.22 42.34 43.42 42.40 43.90 38.95 41.67 38.37 25.39 41.19 24.95 40.76 29.23 41.01 26.86 41.18 28.54 40.76 41.29 42.22 42.46 38.53 38.44 40.55 41.03 26.57 39.22 40.10 23.43 39.24 40.33 28.31 37.87

52.92 50.57 50.56 50.45 54.45 54.45 55.56 55.08 55.57 48.46 52.16 48.59 30.46 51.92 30.23 51.91 36.28 52.10 33.17 51.81 36.08 53.60 53.44 54.06 54.20 49.47 49.92 50.86 51.07 32.21 49.91 50.19 28.43 50.39 50.67 35.00 49.53

61.86 58.49 58.51 58.54 62.53 62.52 63.58 63.35 63.38 54.56 58.94 55.13 33.75 58.99 33.59 59.22 41.08 59.38 37.40 58.69 41.22 61.79 61.43 61.84 61.88 56.65 57.35 57.72 57.70 36.15 56.94 57.03 31.90 57.72 57.61 39.66 57.12

67.88 63.82 63.86 63.94 68.13 68.13 69.06 68.94 68.81 58.74 63.57 59.53 36.00 63.85 35.88 64.25 44.51 64.39 40.36 63.39 44.80 67.28 66.93 67.19 67.16 61.59 62.41 62.53 62.32 38.95 61.79 61.81 34.33 62.71 62.46 42.99 62.27

72.03 67.50 67.54 67.64 72.08 72.09 72.89 72.81 72.63 61.67 66.80 62.57 37.57 67.25 37.47 67.76 46.99 67.88 42.48 66.67 47.31 71.08 70.76 70.94 70.89 65.04 65.92 65.94 65.57 40.95 65.19 65.18 36.05 66.17 65.89 45.39 65.85

Values S°298 and Cp°(T) are based on hindered rotation treatments of hindered rotors. Table S1 lists values obtained using the harmonic oscillator approach.

a

decomposition of M13 into the analogous products. The two C4H7NO isomers (M9, M11), the five doubly unsaturated fourheavy-atom segments (M12, M18, M14, M16, and M20), and the final products (C2H4, H2CO, NCH2, C2H3, HCO, HNCH2) are all detected experimentally from the oxidative decomposition of morpholine:12,13

Table 2. Arrhenius Rate Parameters for the Most Important Reaction in the Decomposition of Morpholine at 1 atm Fitted in the Temperature Range 300−2000 K reaction

A (s−1)

n

Ea/R (K)

morpholine → M4 morpholine → M5 morpholine → M6

4.20 × 1025 2.53 × 1023 6.27 × 1025

−3.36 −2.50 −3.12

41 900 38 100 40 800

In their comprehensive kinetic model based on an analogous model for the pyrolysis of cyclohexane,38 Lucassen et al.12 assumed that the five initial decomposition pathways of the three mophyl radicals proceed with an equal activation energy of 27.7 kcal/mol. In contrast, our calculations found that activation energies for these five pathways take values between 19.3 and 59.5 kcal/mol. Along the same line of enquiry, the initial decomposition of products (M10, M17, M13, M15, and M19) to their corresponding four-heavy-atom segments (M12, M18, M14, M16 and M20) was assumed to occur with an equivalent

IE values for M9 and M11 are calculated to be 8.50 and 8.00 eV, respectively. It follows that the detected C4H7NO isomer12 with a measured IE value of 8.60 eV is most likely to be the M9 moiety. 7708

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Figure 6. Arrhenius plots for the initial reactions in the decomposition of morpholine at 1 atm as a function of temperature (a) and, at 1000 K, as a function of pressure (b).

pressure-dependent reaction rate constants are calculated for the three most plausible exit channels in the initial decomposition of morpholine, namely (morpholine → M4, morpholine → M5, and morpholine → M6). All rate constants are corrected for the plausible contribution of tunnelling based on Eckart’s formula.24 Reaction rate constant for the reaction morpholine → M6 are calculated based on generating minimum energy points (MEPs) along the bond-dissociation pathway within the formalism of variational transition state theory (VTST),41,42 in which the rate constants are minimized as a function of reaction coordinate and temperature. We found that a bond elongation of 2.950 Å provides the longest possible stretching of the H2C−NH bond, in which the structure retains a single imaginary frequency along

activation energy of 28.7 kcal/mol. Our calculated activation energies for these five reactions are generally between 16.8 and 21.0 kcal/mol. It is worthwhile mentioning that H abstraction, bond scissions, and ring-opening reactions have been thoroughly investigated for 2,5-dimethyltetrahydrofuran in a recent study of Simmie; 2,5-dimethyltetrahydrofuran is another important intermediate that arises in the thermal decomposition of biomass.39 3.4. Standard Enthalpies of Formation, Standard Entropies, and Heat Capacities. Table 1 lists values of ΔfH°298 for all species (intermediates, products, and transition structures), estimated based on the calculated reactions enthalpies given in Figures 2−5, the calculated ΔfH°298 of morpholine (Section 3.1), and the experimental ΔfH°298 values for H atom (52.1 kcal/mol), C2H4 (12.5 2.0 kcal/mol), H2CNH (16.0 ± 2.0 kcal/mol), and H2CO (−27.7 kcal/mol) as listed in the NIST thermochemical data compilation.40 While the value of ΔfH°298 is calculated with a reasonable uncertainty limit (0.15 kcal/mol), it should be noted that calculated values of ΔfH°298 for radical and biradical intermediates are expected to incur higher uncertainty values. It was not feasible to design isodesmic work reactions for these species as calculated values of ΔfH°298 for possible reference species are absent from the literature. As explained in Section 2, internal rotations in all species are treated as hindered rotors rather than harmonic oscillators in the calculations of standard entropies and heat capacities. Figure S3 of the Supporting Information illustrates the potential profiles of the rotors. Table 1 also gives calculated values of standard entropies and heat capacities. Standard entropies and heat capacities without the inclusion of treatment of hindered rotors for selected species are given in Table S1. Generally, treatment for internal rotations changes the calculated standard entropies by 0.3−2.5 cal/mol·K in reference to values obtained based on harmonic oscillators. To enable calculations of thermodynamic properties at elevated temperatures by an interested reader, NASA polynomial coefficients are provided in the Supporting Information. 3.5. Reaction Rate Constants. In order to simulate conditions encountered in a real combustion environment,

Table 3. Arrhenius Rate Parameters at the High-Pressure Limit for Reactions Involved in the Decomposition of Morpholine in the Temperature Range 300−2000 K

7709

reaction

A (s−1)

morpholine → M4 morpholine → M5 morpholine → M6 M4 → C2H3NH2 + C2H3OH M5 → NH3 + CH2CHOCHCH2 M2 → M10 M2 → M17 M17 → M18 + H2CNH M18 → C2H3 + H2CO M10 → C2H4 + M12 M12 → HCO + H2CNH M1 → M15 M1 → M13 M15 → H2CO + M16 M16 → C2H3 + H2CNH M13 → M14 + C2H4 M14 → H2CO + HCNH M3 → M19 M19 → H2CO + M20 M20 → C2H4 + NCH2

2.31 × 10 2.47 × 1011 3.12 × 1011 3.10 × 1011 5.23 × 1011 1.05 × 1012 3.34 × 1013 7.25 × 1012 8.76 × 1013 4.23 × 1012 5.22 × 1013 3.14 × 1011 5.00 × 1012 4.33 × 1012 6.11 × 1013 3.11 × 1013 2.82 × 1013 2.90 × 1012 4.18 × 1012 7.00 × 1012 10

n

Ea/R (K)

1.25 1.27 1.24 0.85 0.78 0.65 0.44 0.38 0.55 0.51 0.38 0.95 0.79 0.45 0.37 0.17 0.27 0.54 0.68 0.32

39 400 36 000 38 600 18 750 16 400 12 250 15 000 5 000 18 900 10 700 22 000 29 800 14 800 1 500 22 000 11 500 5 500 9 900 10 700 9 000

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Figure 7. Arrhenius plots for calculated reaction constants for the ring-opening of the three morphyl radicals (a) and subsequent decompositions into four-heavy-atom segments (b). Superscript a indicates the corresponding values adapted by Lucassen et al.12 from a kinetic model for the pyrolysis of cyclohexane.33

intermediate. As shown in Figure 6b, rate constants for these three reactions are predicted to be independent of pressure at a typical combustion temperature of 1000 K and at a pressure as low as 1 atm. Arrhenius parameters for reaction rate constants at the highpressure limit are calculated based on the conventional transition state theory (TST).43 Table 3 lists reaction rate constants for all reactions described in Figures 2−5 at the high-pressure limit. In Figure 7, we compare our calculated reaction constants, for the ring-opening of the three morphyl radicals and subsequent decomposition into four-heavy-atoms segment, with corresponding values adopted by Lucassen et al.12 from a kinetic model of the decomposition of cyclohexane. Generally, our calculated rate constants for the two sets of reactions are higher than corresponding values deployed by Lucassen et al.12 by 1 to 2 orders of magnitude. Accordingly, the insertion of O and N heteroatoms in the C-skeletal structures induces noticeable changes in the kinetics of the decomposition of morpholine in reference to cyclohexane. In view of the prescribed importance of the breakdown reaction in the oxidation of morpholine, reaction rate parameters given in Table 3 should serve as a building block in a comprehensive kinetic model that could account satisfactorily for the product profiles from the oxidative decomposition of morpholine.

the specified reaction coordinate. The formation of this structure is found to be as endothermic as the final product of M6, thus, it has been utilized as a transition structure candidate in calculating the reaction rate constant for the reaction morpholine → M6:

Vibrational frequencies and rotational constants for this transition structure candidate (at a separation of 2.950 Å) are used to derive thermodynamic partition functions. The latter were used to generate a pre-exponential factor for the reaction morpholine → M6. Forward and reverse reaction rate constants for this barrierless reaction are fitted in the wide temperature range of 300 to 2000 K to Arrhenius expressions of 3.12 × 1011T1.24 exp(−39400/T) s−1 and 2.13 × 1010T−0.08 exp(−200/T) s−1, respectively. Treating internal rotations as harmonic oscillators in the transition structure for this ring-opening reaction decreases the reaction rate constants for the forward reaction by factors of 4.0−5.5 within the considered temperature range. This indicates that hindered rotor treatment for internal rotations is necessary to obtain an accurate rate constant for the ring-opening reactions. The effect of this treatment is less profound in the case of ring-closure reactions (i.e., corresponding factors of 1.2−1.4). This observation is expected in view of the presence of internal rotations of N−H and CH2 groups in reactant (M6) and transition structure. Apparent rate parameters at 1 atm for these three most important initial unimolecular reactions are given in Table 2. Dependency of these reactions on temperature and pressure is depicted in Figure 6, parts a and b, respectively. For all considered temperatures and pressures, we found that the initial decomposition of morpholine is solely dominated by intramolecular hydrogen transfer, which preferentially forms the M5

4. CONCLUSIONS Optimized geometries and thermochemical parameters are calculated for all species involved in the breakdown reactions of the self-decomposition of morpholine and its derived morphyl radicals. Calculated values of enthalpy of formation and ring strain energy for morpholine are in good agreement with the corresponding available experimental measurements. Internal rotations in all intermediates and transition structures are treated as hindered rotors in the calculations of standard entropies and reaction rate constants. Kinetic and thermochemical data provided herein should be useful in the pursuit to understand the transformation of nitrogen-containing species in oxidation of 7710

dx.doi.org/10.1021/jp303463j | J. Phys. Chem. A 2012, 116, 7703−7711

The Journal of Physical Chemistry A

Article

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biomass, especially involving the formation of nitrogenates and oxygenates that comprise two to four heavy atoms.

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ASSOCIATED CONTENT

S Supporting Information *

NASA polynomial coefficients, calculated G3MP2B3 enthalpies, Cartesian coordinates, moments of inertia, and vibrational frequencies of all equilibrium and transition state structures. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: (+61) 2 4985-4286. E-mail: Mohammednoor. [email protected]. Present Address

† Also at Chemical Engineering Department, Al-Hussein Bin Talal University, Ma’an, Jordan

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study has been supported by a grant of computing time from the National Computational Infrastructure (NCI), Australia (Project ID: De3) and a fund from the Faculty of Engineering and Built Environment at the University of Newcastle Australia.

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dx.doi.org/10.1021/jp303463j | J. Phys. Chem. A 2012, 116, 7703−7711