Theoretical Study of the Thermal Decomposition of Dimethyl Disulfide

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Theoretical Study of the Thermal Decomposition of Dimethyl Disulfide Aa¨ron G. Vandeputte, Marie-Franc¸oise Reyniers,* and Guy B. Marin Laboratorium Voor Chemische Technologie, Ghent UniVersity, Krijgslaan 281 S5, B-9000 Gent, Belgium ReceiVed: April 14, 2010; ReVised Manuscript ReceiVed: July 19, 2010

Despite its use in a wide variety of industrially important thermochemical processes, little is known about the thermal decomposition mechanism of dimethyl disulfide (DMDS). To obtain more insight, the radical decomposition mechanism of DMDS is studied theoretically and a kinetic model is developed accounting for the formation of all the decomposition products observed in the experimental studies available in literature. Thermochemical data and rate coefficients are obtained using the high-level CBS-QB3 composite method. Among five methods tested (BMK/6-311G(2d,d,p), MPW1PW91/6-311G(2d,d,p), G3, G3B3, and CBS-QB3), the CBS-QB3 method was found to reproduce most accurately the experimental standard enthalpies of formation for a set of 17 small organosulfur compounds and the bond dissociation energies for a set of 10 sulfur bonds. Enthalpies of formation were predicted within 4 kJ mol-1 while the mean absolute deviation on the bond dissociation enthalpies amounts to 7 kJ mol-1. From the theoretical study, a new reaction path is identified for the formation of carbon disulfide via dithiirane (CH2S2). A reaction mechanism was constructed containing 36 reactions among 25 species accounting for the formation of all the decomposition products reported in literature. High-pressure limit rate coefficients for the 36 reactions in the reaction mechanism are presented. The kinetic model is able to grasp the experimental observations. With the recombination of thiyl radicals treated as being in the low-pressure limit, the experimentally reported first-order rate coefficients for the decomposition of DMDS are reproduced within 1 order of magnitude, while the observed product selectivities of most compounds are reproduced satisfactory. Simulations indicate that at high conversions most of the carbon disulfide forms according to the newly identified reaction path involving the formation of dithiirane. 1. Introduction Radical gas phase chemistry of organosulfur compounds is of importance for a wide variety of applications. In particular, small organosulfur compounds are involved in atmospheric chemistry.1-4 They are also used in chemical vapor deposition for the preparation of semiconducting diamond films,5 as CO and coke controlling agents during the thermal cracking of hydrocarbons,6 added to polymerization reactions as an inhibitor,7 initiator,8 or chain controlling agent,9,10 and used as catalyst activators for hydrodesulfurization processes.11,12 During hydrotreatment S- and N-traces are removed from a hydrocarbon feed improving the quality of the gasoline or fuel. Typical hydrotreating catalysts are tungsten or molybdenum sulfides promoted with cobalt and nickel, supported on alumina. In order to activate the molybdenum or tungsten catalyst, a sulfur-rich gas stream is passed over the catalyst at temperatures in the range of 450-650 K.11 Hallie13 reported that activation of the catalyst with dimethyl disulfide (DMDS) increased the hydrotreating activity for CoMo/Al2O3 by 60% compared to a gas phase H2/H2S sulfiding procedure. An important step toward understanding how DMDS enhances the catalytic activity is to know the exact gas phase composition that interacts with the catalyst. An experimental study on the thermal decomposition of DMDS in a nonstirred batch reactor at 589-646 K was performed by Coope and Bryce.14 The authors reported that a complex radical mechanism, initiated by scission of the S-S bond, accounts for the decomposition of DMDS. The main decomposition products were identified as methanethiol * To whom correspondence [email protected].

should

be

addressed,

(CH3SH), dihydrogen sulfide (H2S), ethene (CH2dCH2), and carbon disulfide (CS2). Braye et al.15 studied the thermal decomposition of dimethyl sulfide (DMS) and DMDS in a toluene stream. The authors found that DMDS decomposes at a much lower temperature (735-833 K) than DMS (931-982 K). Dibenzyl was observed during the thermal decomposition of DMS, indicating that the decomposition of DMS proceeds via a radical mechanism. In contrast, no dibenzyl was observed during the decomposition of DMDS. Therefore, Bray et al.15 concluded that the thermal decomposition of DMDS proceeds by a molecular mechanism. Bock and Mohmand16 studied the decomposition of alkyl sulfides using photoelectron spectroscopy in the temperature range 300-1500 K. These authors proposed that S-C scission could be important during the decomposition since larger alkyl substituents on the disulfide lowered the decomposition temperature. Kroto and Suffolk17 also used photoelectron spectroscopy to study the formation of intermediates during the thermal decomposition of DMDS and were able to identify the intermediate formation of thioformaldehyde (H2CdS). Other relevant work has been performed by Shum and Benson.18 These authors reported an experimental study on the thermal decomposition of DMS in a batch reactor at 681-723 K and explained the formation of the main decomposition products by a set of nine reactions. Very recently, Zheng et al.19 presented a detailed experimental and theoretical study on the pyrolysis of diethyl sulfide in a turbulent flow reactor. On the basis of the theoretical calculations, the authors constructed a detailed reaction mechanism that is able to reproduce the experimental data.19 To elucidate the chemistry involved in the thermal decomposition of DMDS, large efforts have been done by Coope and Bryce.14 According to these authors, the thermal decomposition

10.1021/jp103357z  2010 American Chemical Society Published on Web 09/15/2010

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Figure 1. Radical mechanism responsible for the formation of CS2 during the thermal decomposition of dimethyl sulfide according to Shum and Benson.18

of DMDS is initiated by homolytic scission of the S-S bond. The CH3S• radicals start a radical mechanism leading to the formation of mainly CH3SH, H2S, CH2dCH2, and thioformaldehyde. They also suggested that CS2 was formed by the pyrolysis of a polymer residue formed during reaction. A similar radical mechanism was proposed by Bock and Mohmand, but initiated by scission of a S-C bond.16 Shum and Benson18 proposed that the formation of CS2 during the thermal decomposition of dimethyl sulfide can be explained by the radical mechanism presented in Figure 1. Thioformyl radicals add to thioformaldehyde and the formed product further isomerizes via a H shift, after which CS2 is formed by β-scission. An alternative reaction path that leads to the formation of CS2 proceeds via the formation of dithiirane (CS2H2). The involvement of dithiirane in radical reactions of sulfur compounds was initially proposed by Senning.20,21 The first isolable dithiiranes were prepared in 1996 by Ishii et al.,22 and since then, the involvement of dithiiranes in the pyrolysis of sulfur compounds has been demonstrated. For example, Mloston et al.23 were able to identify dithiirane during the thermolysis of 1,2,4-trithiolane. Although experimental studies on the pyrolysis of organosulfur compounds yield important information on their behavior at elevated temperatures,24-26 it is almost impossible to obtain reliable kinetic data for all occurring reactions based on experimental data only since the radical reaction mechanisms involved are very complex. Moreover, experimental data are often obtained within a narrow interval of reaction conditions, making it difficult to extrapolate the data to the temperatures and pressures of interest. Because of the complexity of the reaction mechanisms for the thermal decomposition of organosulfur compounds, alternative approaches have been developed to obtain the required thermodynamic and kinetic data. Benson27 was one of the first to summarize all experimental work on the thermochemistry and kinetics of sulfur-containing molecules and radicals and proposed group additivity schemes from which accurate thermodynamic data could be obtained for various classes of compounds.28,29 Due to the increase in computer capacities, quantum mechanical techniques have become a powerful tool to obtain the required thermodynamic and kinetic data. Several studies have been dedicated to the development of theoretical methods and the validation of these methods for sulfur-containing compounds. Vandeputte et al.30 have shown that feasible but accurate thermochemical data can be obtained using standard composite methods, such as G3 and CBS-QB3. Popular DFT methods, such as B3LYP, BMK, and MPW1PW91, are less accurate and reproduce the experimental standard enthalpies of formation on average within 20 kJ mol-1. Although the BMK functional was especially designed to explore the kinetic behavior of compounds, it is shown throughout literature that this functional performs well in describing properties such as bond dissociation enthalpies31 and isomerization energies.32 DFT methods prove to be a reliable alternative to the more expensive composite methods to obtain rate coefficients for reactions involving organosulfur compounds.30 Theoretical work on the development of reaction mechanisms for the decomposition of sulfur compounds has been performed by Steudel et al.33-35 The authors used the

G3(MP2) and G3X(MP2) method to unravel the thermal decomposition of thiirane, SO2, and tetraamidosulfurane and found good agreement with experimental observations.33-35 As the thermal decomposition of dimethyl disulfide is not yet fully understood, the objective of this paper is to obtain more insight into this reaction mechanism. Therefore, a kinetic model is developed that accounts for the formation of the main decomposition products and succeeds in reproducing most of the experimental observations. The required thermodynamic data for the construction of the reaction mechanism is obtained from CBS-QB3 calculations. Out of a set of five methods, the CBSQB3 method proves to yield the most accurate standard enthalpies of formation, standard entropies, and bond dissociation enthalpies for a selected set of organosulfur compounds. Standard enthalpies of formations, molar entropies, and heat capacities for all 25 sulfur-containing compounds involved in the thermal composition of DMDS are reported and rate coefficients are presented for a mechanism consisting of 36 reactions. Finally, simulations are performed using the CHEMKIN 4.1.1 software package36,37 and the proposed reaction mechanism is validated by comparison with experimental data available in literature. 2. Methodology 2.1. Thermodynamic Properties. All calculations were performed with the Gaussian 03 computational package.38 Electronic energies were calculated according to two DFT methods, i.e., MPW1PW91/6-311G(2d,d,p)39 and BMK/6311G(2d,d,p),40 and three composite methods, i.e., the CBSQB3 complete basis set method,41 the Gaussian-3 theory,42 and the modified Gaussian-3 theory for B3LYP density functional theory (DFT) geometries, also denoted G3B3.43 Standard enthalpies of formation at 298 K, ∆fH°(298 K), are calculated based on experimental atomization energies. The following experimental enthalpies were used: ∆atomH°exp(S; 298 K) ) 276.98 kJ mol-1, ∆atomH°exp(C; 298 K) ) 716.68 kJ mol-1, and ∆atomH°exp(H; 298 K) ) 217.998 kJ mol-1.44 Atomic spinorbit corrections are manually included for the DFT methods and CBS-QB3 in order to make the calculated atomic energies consistent with the experimental heats of formation of the atoms. Montgomery et al. found that the CBS-Q models benefit significantly from inclusion of spin-orbit corrections.41 Atomic spin-orbit corrections amount to -0.4 kJ mol-1 for the carbon atom and to -2.3 kJ mol-1 for the sulfur atom.45 An elaborate example of how standard enthalpies of formation are calculated within the atomization scheme can be found in the Supporting Information. Bond dissociation energies (BDEs) are derived from the enthalpies of formation of the species involved in the homolytic scission of the bond under consideration

BDE(R-X; 298 K) ) ∆fHo(R; 298 K) + ∆fHo(X; 298 K) - ∆fHo(R-X; 298 K) (1) The standard molar entropy S° is obtained from the Gaussian output and is calculated from the total partition function, qtot.

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External and internal symmetry numbers are implicitly taken into account within the Gaussian partition functions. Partition functions within the G3, G3B3, and CBS-QB3 method are calculated on the HF/6-31G(d), B3LYP/6-31G(d), and B3LYP/ 6-311G(2d,d,p) level, respectively. For G3, G3B3, and CBSQB3 the default scaling factor of 0.8929, 0.96, and 0.99 was used. For the MPW1PW91 and BMK method, a scaling factor of 0.99 was applied which is close to the value of 0.9877 advised by Andersson and Uvdal for scaling of DFT/triple-ζ ZPVEs.46 As a default setting, the Gaussian program treats all internal modes as harmonic oscillators (HO). This approximation suits well for vibrations but fails to describe large-amplitude internal motions, such as internal rotations. To obtain more accurate thermodynamic data, the internal modes can be treated as 1D hindered rotors (1D-HR) by solving the Schro¨dinger equation for the internal rotation.47 This 1D-HR treatment has been widely applied for the prediction of accurate thermodynamics.48-52 However, Vansteenkiste et al.53 reported that for thiols and small alkyl sulfides, the 1D-HR treatment does not contribute to more accurate data. In this work, the influence of 1D-HR treatment on the accuracy of the prediction of ∆fH°(298 K) and S°(298 K) is evaluated for a limited set of small sulfur compounds using the method reported by Van Speybroeck et al.47 2.2. Rate Coefficients. Whenever a proper transition state could be located for the studied reaction, the rate coefficient k was calculated using the classical transition state theory in the high-pressure limit. For uni- and bimolecular reactions, k was thus calculated according to eq 2:54

kunimolecular(T) ) κEckart(T)

kbimolecular(T) ) κEckart(T)

kBT qq -∆qE/RT e h qA

(2)

kBT qq -∆qE/RT e h qAqB

with qA, qB, and qq the total molar partition functions per unit of volume of the reactants (A and B) and the transition state, respectively. ∆qE is the electronic activation barrier including zero point vibrational energy (ZPVE). Previously, it was shown that for H abstraction reactions between hydrocarbons, the Eckart tunneling scheme yields more accurate tunneling contributions than the methods of Wigner and Skodje and Truhlar.55 Therefore Eckart tunneling coefficients κEckart(T) are included in the reported rate coefficients.56 For homolytic bond scission reactions, no proper transition state could be located. In order to obtain rate coefficients for these reactions, variational transition state theory (VTST) was used57,58

kVTST(T) ) min s

kBT qVTST(T, s) -∆E(0K)(s)/RT e h qreac

(3)

implying that the rate coefficient is minimized along the reaction coordinate, s. In this work, s has been taken equal to the interatomic distance of the breaking bond. During reaction, a change from singlet to a triplet state occurs. To capture the features of the potential energy surface along the reaction coordinate, CASSCF59 calculations were performed along the reaction coordinate and the obtained energies were rescaled according to eq 4. Rescaling is necessary as the CASSCF bond dissociation energies are generally less accurate than those

calculated with high level composite methods, regardless of the basis set and active space employed.60,61

VCBS-QB3(s) - VCBS-QB3(seq) ) VCBS-QB3(s∞) - VCBS-QB3(seq) (s) - VCASSCF(seq)) (V VCASSCF(s∞) - VCASSCF(seq) CASSCF (4) In eq 4, seq is the equilibrium distance between both fragments in the reactant, i.e., the initial bond length. The potential energy VCASSCF(s) in eq 4 is obtained by cubic spline interpolation to CASSCF/6-311G(2d,d,p) potential energies calculated along the reaction path. ∆E(0 K)(s) is then obtained by adding the ZPVE to the calculated energy surface. It should be noted that the ZPVE also changes along the reaction coordinate. qVTST(T,s) in eq 3 can be written as the products of six contributions qVTST(T, s) = noptqelec(s)qtrans(T)qext.rot(T, s)qvib.cons(T)qvib.ts(T, s)

(5)

In eq 5, qelec, qtrans, qext.rot, qvib.cons, and qvib.ts are the electronic, translational, external rotational, and vibrational partition function of the conserved modes and the vibrational partition function of the transitional modes. nopt in eq 5 accounts for the number of optical isomers. The electronic partition function qelec(s) depends solely on the location of the generalized transition state and equals the electronic degeneracy at s. During homolytic bond scission reactions, the electronic degeneracy increases from 1, corresponding with the singlet state of the reactant, up to a value of 3, corresponding with a triplet state as the molecule dissociates in two radical fragments. qelec(s) was obtained by fitting of eq 6 to the electronic degeneracy calculated at the CASSCF/6-311G(2d,d,p) level along the reaction path

(

qelec(s) ) 1 + 2 1 -

s -R(s2-seq2) e seq

)

2

(6)

with seq the initial bond length. Spin conservation is not expected as the presence of sulfur atoms in molecules increases the likelihood of intersystem crossing.62-64 The translational partition function, qtrans(T), depends solely on the mass of the compound and does not vary as a function of the reaction coordinate. In contrast, the external rotational partition function varies during reaction as the principal moments of inertia change. In this work, a polynomial was fitted to the product of the three moments of inertia obtained from the CASSCF/6-311G(2d,d,p) optimized geometries along the reaction coordinate. This correlation allows qext.rot to be calculated as function of s. During bond scission, six internal modes are converted to translational and rotational degrees of freedom of the two resulting fragments. These modes are often referred to as transitional modes and are contained within qvib.ts. Throughout literature, it has been shown that accurate treatment of these vanishing modes is needed to obtain reliable rate coefficients.65-67 However, accurate treatment of these transitional modes requires knowledge of a large part of the reaction’s potential energy surface and is hence computationally intensive. In this work, the six vanishing modes are treated as described by Grabowy and Mayer.68,69 The internal mode corresponding with the interfragment stretching represents the motion along the reaction coordinate. The lowest frequency mode, which corresponds with a torsion mode, is treated as a free rotor, while the other four

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modes are treated as harmonic oscillators. The frequencies of the oscillators are scaled according to the following equation

ν(s) ) V(seq)e-β(s-seq)

(7)

with ν(s) the frequency at s and seq the equilibrium distance between the two fragments in the reactant. From eq 7, it follows that these four modes vanish exponentially to zero along the reaction coordinate. The parameter β is obtained by fitting of eq 7 to the CASSCF frequencies calculated at the initial bond length and at an interfragmental separation of 300 or 350 pm, depending on the studied bond scission. The remaining nontransitional or conserved modes, whose contributions to the partition function are contained within qvib.cons, were taken to be the same as in the free products and were considered to remain constant along the reaction path. 2.2.1. Arrhenius Parameters. Arrhenius parameters were obtained by a least-squares regression of rate coefficients to the Arrhenius model. To obtain Arrhenius parameters at a temperature T, rate coefficients are calculated at T - 100 K, T - 50 K, T, T + 50 K, and T + 100 K and used for the regression. Pre-exponential factors and activation energies presented throughout this work are hence valid in the temperature interval T ( 100 K. 3. Results and Discussion 3.1. Selection of the Computational Method. In previous work, it was shown that DFT methods and composite methods are promising methods to study the thermodynamics of organosulfur compounds.30 For a small set of S containing molecules, the most accurate rate coefficients were obtained with the BHandHLYP/6-311G(2d,d,p) method, while the most accurate standard enthalpies of formation were obtained with the CBSQB3 method. Among the methods investigated, five methods were identified, i.e., BMK/6-311G(2d,d,p), MPW1PW91/6311G(2d,d,p), G3, G3B3, and CBS-QB3, which produced rather accurate results. A more elaborate comparison between these five methods is presented in this work. Special attention is given to the prediction of thermochemical data for radicals and to the prediction of bond dissociation enthalpies for sulfur bonds. The most accurate method will be selected in order to study the thermal decomposition of DMDS. 3.1.1. Standard Enthalpy of Formation and Standard Molar Entropy. Experimental ∆fH°(298 K) and S°(298 K) of nine sulfur-containing radicals and eight sulfur-containing molecules are presented in Table 1 and Table 2, respectively. ∆fH°(298 K) and S°(298 K) were calculated with the MPW1PW91/6311G(2d,d,p), BMK/6-311G(2d,d,p), G3, G3B3, and CBS-QB3 methods and compared with the experimental data. The results of this study are also shown in Tables 1 and 2. Generally, the calculated values are expressed relative to the experimental data. If the property of a compound is not experimentally determined, the presented ab initio values for this compound are absolute values. The total mean deviation (MD) and total mean absolute deviation (MAD) are given at the bottom of Table 1 and Table 2 for the different levels of theory. Table 1 shows that the three composite methods, i.e., G3, G3B3, and CBS-QB3, accurately reproduce the experimental ∆fH°(298 K) values for the sulfur-containing radicals. The MADs for the three studied composite methods range between 3.2 for CBS-QB3 and 4.5 for G3B3. The two studied DFT methods are less accurate, reproducing the experimental data within approximately 10 kJ mol-1. The mean deviations fluctuate

around zero for the composite methods, while the two DFT methods have the tendency of overestimating the ∆fH°(298 K)s values. With CBS-QB3 the largest discrepancy with the experimental data is retrieved for the hydrogen dithiyl radical, i.e., -8.8 kJ mol-1. This error cannot be attributed to spin contamination as 〈S2〉 amounts to 0.762. The two G3 methods perform well for this compound, reproducing the ∆fH°(298 K) within 2 kJ mol-1. However, both methods overestimate the ∆fH°(298 K) for the two alkyl dithiyl radicals, CH3SS• and C2H5SS•, with approximately 10 kJ mol-1. Considering the expected accuracy obtainable with most DFT methods, the MPW1PW91 method performs well with a MAD of 13.7 kJ mol-1. The BMK functional produces more accurate results with a MAD of 10.2 kJ mol-1. Experimental standard molar entropies could only be retrieved for five sulfur-containing radicals. Table 1 shows that the experimental S°(298 K) values are approached well by the calculated data. All five studied methods perform similarly, yielding MADs around 2 J mol-1 K-1. The discrepancies between calculated and experimental entropies are mainly caused by the neglect of spin splitting. In atoms and linear radicals, both spin and spatial degenerates of the ground state are present and spin-orbit coupling and coupling of the rotation with the orbital motion of the electrons cause significant splitting of the degenerated energy levels.70 This explains for example the deviation of 2 J mol-1 K-1 for atomic sulfur. All theoretical methods used in this work predict a Cs symmetry for the CH3S• radical. This is in agreement with the theoretical results reported by Liu et al.71 Marenich and Boggs72 studied the potential energy surface for the CH3S• radical and showed that inclusion of spin-orbit coupling leads to a ground state having C3V symmetry. Therefore, the calculated entropies for CH3S• in Table 1 include a correction factor -R ln(3) to account for the proper symmetry number. In Table 2, experimental and calculated ∆fH°(298 K) and S°(298 K) values are compared for eight sulfur-containing molecules. The same trends are observed as for the radical set. For enthalpies, the lowest MAD value is obtained with CBSQB3, i.e., 2.4 kJ mol-1. The G3 and G3B3 methods yield somewhat higher MADs, i.e., around 5 kJ mol-1. This result is in agreement with the work of Bond who studied the performance of G3 in reproducing experimental standard enthalpies of formation for a large set of thiols, sulfides, and disulfides.73 The DFT methods systematically overestimate the experimental ∆fH°(298 K)s. Again, the BMK functional performs better than the MPW1PW91 functional: BMK enthalpies of formation are approximately 17 kJ mol-1 higher than the experimental data, while the MPW1PW91 method overestimates the experimental data with 26 kJ mol-1. The large overestimation of the ∆fH°(298 K) for thiophenol with the BMK method is remarkable. It was found that the BMK geometry differs from the B3LYP geometry in that the S-H bond is not in-plane with the phenyl group. The dihedral angle between the S-H bond and the phenyl group within the BMK method amounts to 19°. The stabilizing delocalization due to interaction between the electron pair of the sulfur atom in the 3p orbital perpendicular to the phenyl plane and the π-system of the phenyl group is hence underestimated within this functional. From Table 2, it is once more seen that all five methods yield similar results for S°(298 K). In general, the ab initio data are in good agreement with the experimental observed standard molar entropies, with the exception of HSSH. This discrepancy between experimental and ab initio entropies was also observed in previous work.30

a

Ground state of S: 1s2 2s2 2p6 3s2 3p4 3P2.

TABLE 1: Standard Enthalpies of Formation (∆fH°, kJ mol-1) and Standard Molar Entropies (S°, J mol-1 K-1) at 298 K for Nine Sulfur-Containing Radicals Using MPW1PW91/ 6-311G(2d,d,p), BMK/6-311G(2d,d,p), G3, G3B3, and CBS-QB3 and the Harmonic Oscillator (HO) Approximation

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TABLE 2: Standard Enthalpies of Formation (∆fH°, kJ mol-1) and Standard Molar Entropies (S°, J mol-1 K-1) at 298 K for Eight Sulfur-Containing Molecules Using MPW1PW91/6-311G(2d,d,p), BMK/6-311G(2d,d,p), G3, G3B3, and CBS-QB3 and the Harmonic Oscillator (HO) Approximation

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TABLE 3: Standard Enthalpies of Formation (∆fH°, kJ mol-1) and Standard Molar Entropies (S°, J mol-1 K-1) at 298 K Using CBS-QB3 within the Harmonic Oscillator (HO) Approximation and 1D Hindered Rotor Treatment of All Internal Rotors (1D-HR)

TABLE 4: Bond Dissociation Enthalpies (BDE, kJ mol-1) for 10 Sulfur Bonds at 298 K Using MPW1PW91/6-311G(2d,d,p), BMK/6-311G(2d,d,p), G3, G3B3, and CBS-QB3a

a

For the two studied DFT methods, distinction is made between the unrestricted (U) and restricted open (RO) formalism.

In Table 3, CBS-QB3 ∆fH°(298 K) and S°(298 K) values calculated within the harmonic oscillator approximation and 1D hindered rotor approach are compared. In Table 3, the five components from Table 1 and Table 2 that have internal rotations and for which experimental ∆fH°(298 K) and S°(298 K) values were retrieved, are studied. It is shown that the influence of the 1D-HR treatment on ∆fH°(298 K) is small and amounts, at most, to 0.6 kJ mol-1 for CH3SSCH3. The largest effect is observed on the entropy which can change with up to 4 J mol-1 K-1. It is concluded that for the studied set of small organosulfur compounds, the 1D-HR treatment does not provide more accurate ∆fH°(298 K) and S°(298 K) values. This illustrates that 1D-HR corrections can be omitted when studying

the thermochemistry of the decomposition products of small organosulfur compounds. Similar to this study, Vansteenkiste et al.53 also came to the conclusion that, for smaller alkylsulfides, the 1D-HR treatment does not contribute to more accurate data. 3.1.2. Bond Dissociation Energy. The bond dissociation energy is an important parameter when dealing with radicals and can often assist in the understanding of reactivity patterns. A compilation of experimental and ab initio BDEs can be found in Table 4. For the DFT methods, distinction is made between the unrestricted (U) and restricted open (RO) formalism. Table 4 shows that all three composite methods give good agreement with experiment, yielding a MAD around 7 kJ mol-1. Both DFT methods yield less accurate bond dissociation energies. For

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TABLE 5: CBS-QB3 Bond Dissociation Enthalpies (kJ mol-1) and Mean Bond Dissociation Enthalpies (〈BDE〉, kJ mol-1) at 298 K for S-H, S-C, and S-S Bonds of Various Di-, Tri-, and Tetrasulfides Likely To Be Formed during the Thermal Decomposition of DMDS

UBMK, the MAD amounts to 10.0 kJ mol-1, which is at least 2 kJ mol-1 more than those obtained for CBS-QB3, G3, and G3B3. For UMPW1PW91, a MAD of 19.7 kJ mol-1 is retrieved. For this functional, the restricted open formalism is capable of predicting more accurate BDEs; the MAD for ROMPW1PW91 is almost 6 kJ mol-1 lower than the value obtained with UMPW1PW91. However, the opposite is observed for the BMK functional. For ROBMK a MAD of 11.3 kJ mol-1 is obtained which is slightly higher than the value obtained for UBMK. It can also be seen from Table 4 that all three composite methods overestimate the BDE for scission of the C-S bond in thiophenol, probably caused by the high spin contamination observed in the phenyl radical ( ) 1.24-1.41). Also remarkable is that the CBS-QB3 method succeeds in predicting much more accurate BDEs for S-S bonds than G3 and G3B3. The G3 methods systematically underestimate the BDE of a S-S bond with approximately 10 kJ mol-1. CBS-QB3 BDEs were calculated for hydrogen and methylsubstituted di-, tri-, and tetrasulfides. The BDEs are a measure for the bond strengths and can thus be used to identify the weakest bonds. The results are presented in Table 5. From this table it can be seen that sulfur atoms weaken adjacent bonds. For example, each adjacent sulfur atom decreases the BDE of a S-S bond with approximately 60 kJ mol-1. This decrease is caused by electronic effects: the lone pairs of the adjacent sulfur atoms stabilize the formed radical and hence lead to lower BDEs. The weakening effect of adjacent sulfur atoms is also observed for the S-H and S-C bonds. For example, the BDEs of the S-H (364.3 kJ mol-1) and S-C bond (315.4 kJ mol-1) in CH3SH are approximately 60 kJ mol-1 higher than the BDEs for S-H and S-C bonds of all polysulfides. The data presented in Table 5 also confirm that, in contrast to tri- and tetrasulfides which decompose by scission of an S-S bond, DMDS predominantly decomposes by scission of a S-C bond as suggested by Bock and Mohmand.16 The calculated BDE for a S-C bond in DMDS is 24 kJ mol-1 lower than the one obtained for a S-S bond. The presented BDEs correspond well with other

computational data.74-76 For example, Zou et al.76 studied BDEs of polysulfides with CBS-Q, G3, G3B3, CCSD(T), CBS-4 M, and ROMP2. Their CBS-Q results are in excellent agreement with the CBS-QB3 data presented in this work. The authors report CBS-Q BDEs for HSS-SSH and HSSS-SH of 176.1 and 220.9 kJ mol-1,76 respectively, which agree well with the values of 175.0 and 219.0 kJ mol-1 found with CBS-QB3. 3.2. Thermal Decomposition of DMDS. On the basis of experimental work available in literature and our results obtained with CBS-QB3, a reaction mechanism was constructed (see Figure 2) that is able to explain the formation of the main intermediates and products that have been identified during the thermal decomposition of DMDS. Thermodynamic data for all the compounds considered in the reaction mechanism are given in Table 6. Four key reaction families can be distinguished: (a) bond dissociations and their reverse recombination reactions, (b) radical additions and their reverse β-scissions, (c) hydrogen abstractions, and (d) homolytic substitution reactions on sulfur atoms. Bond dissociation reactions can be considered as the initiation reactions and are often identified as the rate-determining steps of radical reaction mechanisms. Radical additions, H abstractions, and substitution reactions are the most important propagation reactions and play a critical role in defining the product distribution. The reaction mechanism presented in Figure 2 contains 36 reactions, i.e., 4 bond scissions, 9 β-scission/addition reactions, 17 H abstractions, 5 substitution reactions, and 1 unimolecular elimination reaction. Rate coefficients and Arrhenius parameters at 600 K for all reactions are given in Table 7. 3.2.1. Initiation Reactions. The thermal decomposition of DMDS can be initiated by either S-S, C-S, or C-H cleavage (R1-R3, see Figure 2). Rate coefficients for these three reactions were obtained from variational transition state theory. As discussed in the methodology section, VTST requires knowledge of the potential energy as a function of the reaction coordinate in order to be able to calculate rate coefficients for the bond scission/radical recombination reactions. In Figure 3 potential



Figure 2. Proposed reaction mechanism for the thermal decomposition of DMDS.

energy profiles are presented for S-S, C-S, and C-H cleavage as a function of the interfragmental distance between the two breaking/bonding fragments. Clearly, the highest bond dissociation energy is obtained for scission of the C-H bond. The potential energy increase during C-H scission is at least 100 kJ mol-1 higher than for the other two scission reactions. Besides bond scission, Braye et al.15 suggested that DMDS can also decompose according to a nonradical mechanism. A plausible nonradical mechanism for the thermal decomposition of DMDS is the unimolecular elimination reaction with the formation of CH3SH and H2CdS (R36).

Rate coefficients for the three unimolecular bond scission reactions and the unimolecular elimination reaction are shown in Figure 4 for temperatures ranging from 300 to 1000 K. From Figure 4, it can be seen that cleavage of the C-S (R1) and S-S (R2) bond are the main initiation reactions. At 300 K, scission of the S-C bond proceeds almost 3 orders of magnitude faster than scission of the S-S bond. However, higher temperatures favor the scission of the S-S bond, and at 1000 K the rate coefficients for both reactions are almost equal. The rate coefficients for scission of a C-H bond (R3) and the unimolecular elimination reaction (R36) are at least 2 orders of magnitude smaller than those obtained for (R1). Both reactions are hence unlikely to contribute to the initiation of the decomposition of DMDS. Nevertheless, the reverse reactions,

such as for example the radical recombination reaction of H• with CH3SSC•H2, can still play a role during the decomposition. High-pressure limit rate coefficients and Arrhenius parameters at 600 K for the four initiation reactions and their reverse reactions are given in Table 7. The data illustrate that for the three scission reactions the calculated activation energies are very close to the ∆rH°(298 K) values, while the pre-exponential factors vary around 1016-1017 s-1. The calculated preexponential factors are in good agreement with values reported by Zheng et al., i.e., a pre-exponential factor of 2.0 × 1016 s-1 for scission of a S-C bond in diethyl sulfide.19 The activation energies for the radical recombination reactions are small and amount to approximately 2 kJ mol-1. The activation energy at 600 K for the molecular elimination reaction (R36) amounts to 263 kJ mol-1, which is almost equal to the activation energy for scission of the S-S bond. The pre-exponential factor is however 5 orders of magnitude smaller, explaining the low rate coefficients obtained for this reaction. Also, the reverse reaction is unlikely to have an important influence on the reaction mechanism as the rate coefficient for this reaction amounts to only 5.9 × 10-10 m3 mol-1 s-1. From the data in Table 7 it can be expected that decomposition of DMDS becomes important from 650 K onward, in agreement with experimental observations by Bock and Mohmand.16 At this temperature the rate coefficient for initiation of DMDS amounts to 1 × 10-3 s-1. Recent work on the modeling of the pyrolysis and oxidation of small sulfur compounds shows that the developed reaction mechanisms are very sensitive to the rate of S-S bond scission.60,77,78 Sendt et al.78 showed that good agreement with

10540


Vandeputte et al.

TABLE 6: CBS-QB3 Standard Enthalpy of Formation at 298 K (∆fH°, kJ mol-1), Standard Molar Entropy at 298 K (S°, J mol-1 K-1), and Standard Heat Capacities (cp°, J mol-1 K-1) for All Compounds Presented in Figure 2

experimental data in the pressure range 40-300 kPa can be obtained when the recombination reaction of two hydrogen thiyl radicals is treated as being in the low pressure limit. This result indicates that recombination reactions involving sulfur centered radicals, e.g., (R2), have a high falloff pressure. The pressuredependence of (R2) was evaluated using the equations derived by Wong et al.79 These equations allow estimating the lowpressure limit rate coefficient k0 and require Ea and A for each reaction channel, the collision rate and the collision efficiency. Details of the calculation can be found in the Supporting Information. In analogy with the work of Sendt et al.60 for reactions involving sulfur and oxygen atoms, collision efficiencies were taken from the work of Troe80 for the reaction H + O2 (+ M) f HO2 (+ M). The resulting third-order rate coefficients in the low-pressure limit for (R2) are presented in Figure 5, where they are compared with the third-order rate coefficients reported by Cerru et al.77 and Sendt et al.78 for recombination of two hydrogen thiyl radicals. Sendt et al.78 used the master equation method to obtain rate coefficients for this reaction, while Cerru et al. set the rate coefficient to half of the value obtained for recombination of two OH radicals. Figure 5 illustrates that despite the large uncertainties on the collision

efficiency, the calculated rate coefficients agree within a factor of 3 with the rate coefficients reported by Cerru et al.77 3.2.2. Decomposition Pathways of DMDS. The radicals formed by scission of a S-S, S-C, or C-H bond (R1-R3) can abstract a hydrogen atom from DMDS resulting in the formation of methyldisulfanylmethyl radicals (CH3SSC•H2). Kinetic parameters at 600 K for the H abstraction reactions from DMDS by H•, C•H3, CH3S•, CH3SS•, and HS• can be found in Table 7 (R5-R9). The highest rate coefficient is obtained for H abstraction by H•, followed by HS•, C•H3, CH3S•, and finally CH3SS•. Especially CH3SS• has a low affinity for H abstraction. At 600 K, the rate coefficient for R8 amounts to merely 5.0 × 10-4 m3 mol-1 s-1, which is 8 orders of magnitude smaller than that obtained for the hydrogen abstraction from DMDS by H•. CH3SS• radicals are stabilized by the formation of a threeelectron bond between the two terminal sulfur atoms.81 This stabilization in the CH3SS• radical results in an exceptionally high activation energy for the hydrogen abstraction reaction, i.e., 111 kJ mol-1. Pre-exponential factors for the H abstraction reactions from DMDS vary around 107 m3 mol-1 s-1. The results obtained for (R7-R9) indicate that rate coefficients for abstraction of a hydrogen atom bound to a S atom by a carbon centered

TABLE 7: CBS-QB3 ZPVE Included Energy Barrier at 0 K (∆qE, kJ mol-1), Standard Reaction Enthalpy (∆rH°, kJ mol-1), and Entropy (∆rS°, J mol-1 K-1) at 298 K, Arrhenius Parameters (log A, s-1 or m3 mol-1 s-1 and Ea, kJ mol-1), and Corresponding Rate Coefficients (k, s-1 or m3 mol-1 s-1) at 600 K for the Reactions Depicted in Figure 2a

Thermal Decomposition of Dimethyl Disulfide J. Phys. Chem. A, Vol. 114, No. 39, 2010 10541

Arrhenius parameters and rate coefficients are calculated within the HO approximation and include Eckart tunneling corrections.


a

TABLE 7: Continued

10542 Vandeputte et al.


Figure 3. Potential energy surfaces obtained from eq 4 for scission of S-C (s), S-S ( · · · ), and C-H (s • s) bonds in DMDS. s is the bond length of the breaking bond.


Figure 5. Third-order rate coefficients in the low-pressure limit for the recombination of two thiyl radicals: rate coefficients obtained for (R2) using the formulas of Wong et al.79 (solid black line) and rate coefficients proposed by Cerru et al.77 (dotted line) and Sendt et al.78 (dashed line) for recombination of two hydrogen thiyl radicals.

and 2.9 s-1. Hence, it can be concluded that the methyldisulfanylmethyl radicals will mainly decompose by β-scission leading to the formation of the intermediate thioformaldehyde and CH3S• radicals. Experimental data support that H2CdS is one of the most important intermediates formed during the pyrolysis of DMDS.17 The radicals formed in the initial stage of the decomposition of DMDS, i.e., methyl and CH3S•, can add to H2CdS (R22, R24, R25). The addition of methyl to thioformaldehyde leads to the formation of CH3CH2S• (R22), while addition of CH3S• yields CH3SSC•H2 (R24) or CH3SCH2S• radicals (R25).

Figure 4. Arrhenius plot comparing the rate coefficients of the four reactions initiating the decomposition of DMDS, i.e., homolytic scission of S-C (s), S-S ( · · · ), and C-H (s • s) bonds and molecular elimination leading to H2CdS and CH3SH (- - -).

radical vary between 1 × 104 and 1 × 105 m3 mol-1 s-1. This result is in agreement with the rate coefficients of 2.5 × 104 and 4.0 × 104 m3 mol-1 s-1 reported by Zheng et al. for the hydrogen abstraction by C•H3 from H2S and CH3CH2SH, respectively.19 Methyldisulfanylmethyl radicals (CH3SSCH•2) can decompose via β-scission yielding H2CdS and CH3S• (R24), undergo an intermolecular substitution reaction to dithiirane (R31), or isomerize to CH3SCH2S• (R33).

The rate coefficients at 600 K for these three competing unimolecular reactions amount to respectively 1.5 × 108, 2.1,

Addition of methyl to H2CdS can also occur at the S atom of the CdS double bond, leading to the formation of CH3SC•H2 radicals. In contrast to CH3CH2S•, CH3SC•H2 radicals cannot isomerize via a H shift and they can hence only participate in hydrogen abstraction reactions leading to the formation of dimethyl sulfide. As no dimethyl sulfide has been observed during the thermal decomposition of DMDS,15 it is assumed that the formation of CH3SC•H2 radicals will not significantly contribute to the reaction mechanism. Reactions involving CH3SC•H2 radicals were therefore omitted. The addition of methyl and CH3S• to H2CdS initiates the formation of ethene and carbon disulfide, respectively. Addition of CH3S• to H2CdS leads to CH3SCH2S• or CH3SSC•H2 radicals (R24 and R25) which can react in a subsequent step to dithiirane and methyl (R31 and R32).

10544


H abstraction from dithiirane or intramolecular S-S cleavage followed by β-scission results in the formation of CS2. The formation of ethene starts with the addition of a methyl radical to H2CdS, forming an ethyl thiyl radical, CH3CH2S• (R22). Successive intramolecular H abstraction (R20) and β-scission (R23) result in ethene and a hydrogen thiyl radical, HS•.

The data presented in Table 7 show that the rate coefficients obtained for addition of CH3S• radicals to H2CdS (R24, R25) are higher than the one obtained for addition of C•H3 (R22). At 600 K, the rate coefficients for addition of CH3S• to H2CdS amount to approximately 1 × 107 m3 mol-1 s-1, while for addition of C•H3 a value of 1 × 106 m3 mol-1 s-1 is obtained. The activation energies for addition to H2CdS are small and amount to maximum 13 kJ mol-1 for (R22). Table 7 also illustrates that the β-scissions in CH3SSC•H2 and CH3SCH2S• leading to CH3S• and H2CdS can be expected to proceed very fast. Rate coefficients at 600 K for these reactions range around 107 s-1. This is almost 7 orders of magnitude larger than the rate coefficient found for β-scission of CH3CH2S• (R22). CH3CH2S• radicals are more likely to decompose by a H shift (R20) followed by β-scission (R23). From Table 7, it can be seen that the H shift in CH3CH2S• (R20) proceeds more than a factor of 10 faster than the competitive β-scission reaction (R22). The C•H2CH2SH radicals formed in this way then quickly decompose to CH2dCH2 and HS• (R23). The rate coefficient for this reaction is almost 4 orders of magnitude larger than the one obtained for the competitive H shift from C•H2CH2SH to CH3CH2S• (R20). H2CdS can also be consumed by hydrogen abstraction reactions which lead to the formation of HC•dS radicals (R15-R19). The data presented in Table 7 illustrate that hydrogen abstractions from H2CdS are 16 kJ mol-1 more exothermic than abstractions from DMDS. As a result, the activation energies obtained for abstraction of a hydrogen atom from H2CdS are approximately 10 kJ mol-1 lower. As for abstraction from DMDS, the pre-exponential factors range around 107 m3 mol-1 s-1. The rate coefficients at 600 K for hydrogen abstraction from H2CdS are up to 2 orders of magnitude higher than the ones obtained for hydrogen abstraction from DMDS. In particular sulfur-centered radicals show a high affinity to abstract hydrogen atoms from H2CdS: the highest rate coefficient is obtained for hydrogen abstraction by HS•. The formation of carbon disulfide is considered to occur according to two different reaction paths: a first reaction path is initiated by the addition of HC•dS to thioformaldehyde while a second path leading to CS2 involves the decomposition of dithiirane. The HC•dS radicals can react with H2CdS and form SdCHSC•H2 (R29).

The rate coefficient at 600 K for this addition reaction amounts to 2.9 × 104 m3 mol-1 s-1, which is at least a factor 30 lower than the values obtained for addition of methyl and sulfur-centered radicals. H shift in the SdCHSC•H2 radicals will

Vandeputte et al. lead to the production of SdC•SCH3 radicals (R21) which can decompose by β-scission to CS2 and methyl (R30).

This intramolecular hydrogen shift in SdCHSC•H2 is highly activated (Ea ) 143.4 kJ mol-1) resulting in a rate coefficient of 6 × 10-1 s-1. The rate coefficient for the competitive β-scission reaction of SdCHSC•H2 leading to H2CdS and H•CdS is almost 2 orders of magnitude higher. These results indicate that SdCHSC•H2 radicals will mainly decompose by β-scission and to a smaller extent undergo H shift to form SdC•SCH3, hampering the production of CS2 according to this reaction path. A competitive reaction path toward CS2 involves the formation of three-membered ring structures containing two sulfur atoms, i.e., dithiiranes. To the best of our knowledge, dithiirane has not been experimentally observed during the thermal decomposition of DMDS. However, the CBS-QB3 results indicate that this compound could be easily formed during the decomposition of DMDS. Dithiirane decomposes by homolytic scission of the S-S bond (R4) or can participate in reactions with other radicals such as H abstraction reactions (R10-R14) and substitution reactions (R31, R32).

No proper transition state could be located for (R4). For this reaction, a late transition state is expected, and in this particular case, the rate coefficient for the reverse reaction can be roughly approximated by kBT/h. The activation energy for the forward reaction was set equal to the BDE, while the pre-exponential factor was obtained from thermodynamical consistency. This approximation leads to a rate coefficient of 9 × 10-3 s-1 at 600 K for scission of a S-S bond in dithiirane. This is almost 3 orders of magnitude higher than obtained for scission of a S-S bond in DMDS (R2). The decomposition of dithiirane to CS2 can also be initiated by a hydrogen abstraction (R10-R14). Table 7 illustrates that rate coefficients for H abstraction reactions from dithiirane are of the same order of magnitude as those for H abstraction from DMDS. Besides H abstraction reactions, the two radical substitution reactions (R31, R32) can also be expected to play an important role in the reaction mechanism. For instance, similar rate coefficients are obtained for H abstraction by C•H3 (R11) and radical substitution with C•H3 (R31). The radicals formed by H abstraction from dithiirane or by scission of the S-S bond in dithiirane can decompose by β-scission reactions (R26-R28).



TABLE 8: Simulated Gas Phase Composition (mol %) after 2 h of Thermal Decomposition of DMDS in a Homogeneous Batch Reactor at 10 kPa mol % compound

600 K

620 K

640 K

660 K

680 K

700 K

CH3SH H2CdS dithiirane H2S CS2 C 2 H4 H2 + CH4 CH3SSCH3

7.9 7.5 0.7 2.9 0.3 2.9 0.1 75.9

13.6 10.6 2.8 9.2 1.3 9.2 0.1 48.0

15.9 8.1 4.7 18.3 3.6 18.2 0.3 21.0

15.7 4.0 3.5 25.4 7.1 24.6 0.5 5.6

13.4 1.6 1.5 29.8 9.6 27.5 0.9 1.1

11.1 0.8 0.5 32.3 10.7 28.7 1.2 0.3

For (R26), no transition state could be located and a similar strategy was applied as for S-S bond scission in dithiirane. The rate coefficients obtained for β-scission of a C-H bond in SdCHsS• (R28) and S•sCH2sS• (R27) amount to 1.3 × 102 and 6.3 s-1, respectively. H• radicals produced by these reactions will mainly participate in radical substitution reactions (R34, R35).

Figure 6. Maximum rates of production Rv,max for the different products formed during the thermal decomposition of DMDS in the temperature range 600-700 K: DMDS (s), H2CdS (- -), dithiirane (gray line), CH4 ( · · · ), C2H4/H2S (---), CH3SH (s••s), and CS2 (-•-). The values displayed for DMDS are -Rv,max. High-pressure limit rate coefficients from Table 7. Simulation conditions: homogeneous batch reactor, initial mole fraction DMDS ) 100 mol %, p ) 10 kPa.

TABLE 9: Experimental and Simulated Gas Phase Compositions (mol %) after 2 h of Thermal Decomposition of DMDS in a Homogeneous Batch Reactor at 10 kPaa

The rate coefficients obtained for these reactions are slightly (( a factor of 3) higher than those for addition reactions to CdS bonds (R27, R28) and at least 10 times higher than the ones obtained for H abstractions from DMDS (R5-R9) and dithiirane (R10-R14). The rate coefficient obtained for the homolytic substitution by hydrogen on DMDS (R34) is in good agreement with the high-pressure limit value of 1.5 × 107 m3 mol-1 s-1 reported by Sendt et al.78 for homolytic substitution by a hydrogen radical on HSSH. 3.3. Model Simulations of the Thermal Decomposition of DMDS. The rate coefficients presented in Table 7 were used to simulate the thermal decomposition of DMDS. The CHEMKIN thermo and kinetics input files used for the simulations can be found in the Supporting Information. Simulated gas phase compositions for the decomposition of DMDS in a homogeneous batch reactor at a pressure of 10 kPa for temperatures ranging from 600 to 700 K are presented in Table 8. It can be seen that the main decomposition products of DMDS are methanethiol (CH3SH), H2S, and ethene. At lower temperatures, the model predicts the formation of significant amounts of thioformaldehyde (H2CdS) and dithiirane. H2CdS yields can amount up to more than 10 mol %, while the maximum dithiirane yield amounts to approximately 5 mol %. Both compounds are intermediate products and decompose at higher temperatures. The decreasing CH3SH yield from 680 K onward can be attributed to the increased selectivity toward CS2. As shown in Figure 2, the formation of CS2 is accompanied by the production of hydrogen radicals (R28), which have a high affinity to participate in homolytic substitutions on sulfur atoms (R34, R35). Hydrogen radicals reacting with CH3SH lead to the production of H2S and methyl radicals. This also supports the observation of Bray et al.13 that at higher temperatures methane is formed during the thermal decomposition of DMDS. Maximum rates of production, Rv,max, in the temperature range 600-700 K for the various decomposition products are depicted in Figure 6. For most compounds a linear relation is found between Rv,max and 1/T. It can be seen from Figure 6 that the

compound CH3SH H2CdS dithiirane H 2S CS2 C 2H 4 H2 + CH4 thiophene CH3SSCH3

Coope and Bryce,14 590 K

simulation 1, 646 K

simulation 2, 623 K

35

16 7 5 21 5 21 0

33 2 6 17 9 17 0

15

15

25 9 15 0 1 15b

a

For simulation 1 the high-pressure limit rate coefficients presented in Table 7 are used, while in simulation 2 the recombination of two methylthiyl radicals is treated as being in the low-pressure limit. b From disulfide test.

production rate for H2CdS almost equals the decomposition rate of DMDS indicating that DMDS decomposes mainly by hydrogen abstraction reactions (R5-R9) followed by β-scission (R24). The rates of production of CH3SH show the lowest temperature dependence, indicating that at higher temperatures the selectivity toward CH3SH decreases in favor of other compounds such as H2S, CS2, and CH4. Experimental data on the thermal decomposition of DMDS has been reported by Coope and Bryce.14 The authors studied the thermal decomposition of DMDS in a heated 250 mL Pyrex reactor at 590 K and an initial DMDS pressure of 10 kPa. After 2 h of reaction, the partial pressures of various volatile constituents were analyzed. The authors report that uncertainties on the measured partial pressures are large, as the sum of the partial pressures of all compounds adds up to 120% of the total pressure. As a result, the uncertainties on the experimental mole fractions presented in Table 9 are large. In particular the values reported for carbon disulfide and hydrocarbons are known within 1 order of magnitude only.14 The simulations performed in this work were conducted using a homogeneous batch reactor model, hence assuming that no temperature and concentration gradients

10546


Figure 7. Contributions of (R28) (dark gray) and (R30) (light gray) to the simulated CS2 yield (mol %) in the temperature range 600-700 K. High-pressure limit rate coefficients from Table 7. Simulation conditions: homogeneous batch reactor, initial mole fraction DMDS ) 100 mol %, p ) 10 kPa, t ) 7200 s.

are present in the reactor. However, the experiments were conducted without the use of a mixing device, and temperature and concentration gradients can hence be expected. Agreement with the experimental data will also be hampered by the fact that all reported rate coefficients were calculated within the highpressure limit while the experiments were conducted at a pressure of 10 kPa only. In Table 9 the simulated results are compared with the data obtained by Coope and Bryce14 at 590 K. Simulations were performed at higher temperatures in order to obtain the same DMDS conversion as reported by the authors. From Table 9 it can be seen that the model underestimates the selectivity toward methanethiol, while reasonably good agreement is obtained for H2S and ethene. The underestimation of the methanethiol yield can be explained by an overestimation of the rate coefficient for CH3S• + CH3S• recombination (R2). Using the low-pressure limit rate coefficients reported by Cerru et al.77 for recombination of two hydrogen thiyl radicals (k0 ) 8.7 × 106 T-0.76 m6 mol-2 s-1), much better agreement is obtained with the experimental data. This is also shown in Table 9. When (R2) is modeled as being in the low pressure limit, the model reproduces accurately the selectivity toward all main decomposition products. The largest discrepancy is obtained for H2S, whose yield is underestimated with 8 mol %. Coope and Bryce14 observed a first-order dependence of the rate of disappearance of DMDS and estimated a pre-exponential factor of 2 × 1013 s-1 and an activation energy of 188 ( 20 kJ mol-1. The activation energy and pre-exponential factor calculated from the simulated disappearance rates for DMDS (Rv,max) amount to 222 kJ mol-1 and 1.2 × 1015 s-1, resulting in rate coefficients which are approximately 10 times smaller than experimentally observed. By using the low-pressure limit rate coefficients for (R2), the decomposition of DMDS proceeds almost 10 times faster. In this case, the activation energy and pre-exponential factor amount to 175 kJ mol-1 and 2 × 1012 s-1, in good agreement with the experimental values. The simulated CS2 yield after 7200 s of reaction obtained in the temperature range 600-700 K using the high-pressure limit rate coefficients is shown in Figure 7. The contribution of the two different reaction paths is shown, i.e., the contribution of

Vandeputte et al.

Figure 8. Simulated H2CdS (s), dithiirane ( · · · ), and CS2 (---) yield as function of DMDS conversion. High-pressure limit rate coefficients from Table 7. Simulation conditions: homogeneous batch reactor, initial mole fraction DMDS ) 100 mol %, p ) 10 kPa, T ) 650 K.

(R28) and (R30) to the CS2 yield. Figure 7 illustrates that at lower temperatures (

Theoretical Study of the Thermal Decomposition of Dimethyl Disulfide

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