Roaming radical kinetics in the pyrolysis and combustion of ethanol

Transcription

1 Paper # 070RK-157 Topic: Reaction Kinetics 8 th U. S. National Combustion Meeting Organize by the Western States Section of the Combustion Institute an hoste by the University of Utah May 19-22, 2013 Roaming raical inetics in the pyrolysis an combustion of ethanol A. G. Vaneputte, L. B. Haring, Y. Georgievsii, S. J. Klippenstein Chemical Sciences an Engineering Division, Argonne National Laboratory 9700 South Cass Avenue, Builing 200, Argonne, IL sj@anl.gov 1. Introuction The importance of roaming uring the pyrolysis an combustion of ethanol is stuie. High level multi-reference methos (CASPT2) are use to map the potential energy surface an to locate the various transition states an intermeiate van er Waals complexes. A combination of trajectory an statistical theory stuies are use to preict the effect of roaming on both the ecomposition an bimolecular inetics. The exact location of the van er Waals complexes an subsequent barriers to proucts, play a pivotal role uring roaming as recent wor inicates that most reactive trajectories pass through these wells. For the issociation of ethanol to methyl an hyroxymethyl, a roaming transition state coul be ientifie at an interfragment istance of 330 pm. Its imaginary vibrational moe of approximately 100 cm -1 correspons with an inversion motion of the methyl fragment. Once this roaming transition state has been crosse, the methyl fragment enters a part of the potential energy surface that is characterize by a van er Waals complex, with a well epth of approximately 8 J mol -1. This van er Waals complex connects to a relatively tight sale point for isproportionation leaing to the formation of methane an formalehye. This isproportionation transition state has a potential energy that is only 3 J mol -1 lower than the raical asymptote an proves to be the bottlenec for the irect ecomposition of ethanol to methane an formalehye. Owing to the tightness of the transition state for isproportionation, roaming is preicte to contribute at most 2% to the ecomposition of ethanol. A larger effect of roaming is expecte for the bimolecular reaction between methyl an hyroxymethyl. Trajectory simulations show that the relatively tight transition state for isproportionation forces most of the incoming raicals to follow a roaming path towars the recombination channel. Approximately a ecae ago, a new ecomposition mechanism was experimentally iscovere accoring to which two raical fragments react with each other, after nearly issociating. This new mechanism is referre to as roaming because an intermeiate step in this mechanism is the seemingly free motion of the fragments aroun each other. As no clear reaction path exists an classical transition state theory hence breas own, specialize theoretical framewors were evelope to stuy this new reaction mechanism (Klippenstein et al. 2011). To ate, roaming mechanisms have been experimentally an theoretically stuie in the ecomposition of alehyes an alanes. However, roaming contributions to the ecomposition an combustion of alcohols remain unexplore. Ethanol is seeing wiesprea use as a liqui fuel blening agent for gasoline. It is nown as a safe, competitively price, clean an accessible renewable fuel. Due to its high octane number, higher heat of vaporization an high laminar flame spee it is consiere one of the most suite alcohols to be use in spar ignition engines. Most moern cars can hanle ethanol blens up to 20% without the nee for special conversion its. Its utility as a renewable fuel has spare an increase interest in the pyrolysis an combustion of this component. An improve unerstaning of its ecomposition mechanism will contribute to the fielity of etaile combustion networs that, in their turn, can be the footing of improve engine esign efforts. It also serves as a small prototype for larger alcohols, such as butanol, that may fin utility as secon generation biofuels. Recent stuies have shown that roaming mechanisms are universal an can significantly alter the ecomposition mechanism. In particular, for branche alanes it has been shown that roaming can account for up to 20% of the total

2 ecomposition (Sivaramarishnan et al. 2012). By offering an alternative non-raical ecomposition path, roaming will alter the raical pool an hence influence various characteristics important for combustion, such as the flame spee an ignition elay. Base on G2M calculations, Par et al. (2002) suggeste 11 possible ecomposition pathways for ethanol. The three main ecomposition channels are: (a) C 2 H 5 OH C 2 H 4 + H 2 O (b) C 2 H 5 OH CH 3 + CH 2 OH (c) C 2 H 5 OH CH 3 CH 2 + OH At lower temperatures ethanol will mainly ecompose by the molecular elimination of water. The high temperature ecomposition is mainly controlle by a raical chain process initiate by reactions (b) an (c). Dryer an co-worers stuie the ecomposition of ethanol at 950 K in a variable-pressure flow reactor (Li et al. 2001). It was foun that the main ecomposition proucts are H 2 O, C 2 H 2, CH 4, an CH 3 CHO. Recently, etaile shoc-tube measurements of rate coefficients for ethanol ecomposition have been reporte by Sivaramarishnan et al. (2010) an Wu et al. (2011). Both groups mae use of H-atom atomic resonance absorption spectrum (ARAS) etection. Sivaramarishnan et al. (2010) combine this with OH optical absorption, allowing them to erive rate coefficients for pathway (c) in aition to (a) an (b). Sivaramarishnan et al. (2010) also presente an ab initio transition state theory base master equation analysis of the ecomposition. These authors suggeste that a roaming pathway from the CH 3 + CH 2 OH asymptote woul provie an alternative route to CH 4 + CH 2 O. However, the ifficulty of treating this channel preclue their treatment of its inetics. The present wor aims to fill this gap an also aims at increasing our general unerstaning of the roaming mechanism. 2. Methos Electronic Structure Calculations Geometry optimizations an zero-point energy evaluations for the roaming region were mainly performe with the CASPT2(2,2)/aug-cc-pVTZ metho. The active space inclues the σ an σ* orbitals of the C C bon, which evolve to the two raical orbitals at larger interfragment istances. Final energies were obtaine from complete basis set extrapolation of the aug-cc-pvtz an aug-cc-pvqz results. For those cases where the multi-reference character of the wave function is small, aitional calculations were performe at the CCSD(T) level of theory. The CCSD(T) geometry optimizations were performe using the cc-pvtz basis set while final energies are obtaine from extrapolation to the complete basis set limit using aug-cc-pvtz an aug-cc-pvqz energies. All electronic structure calculations were performe with the Molpro (2010) ab initio pacage. Transitional Moe Potential Energy Surface The statistical an trajectory calculations of the roaming inetics require a 6-imensional potential energy surface escribing the interactions between rigi CH 3 an CH 2 OH fragments. This potential was obtaine from 6-imensional linear Lagrange interpolation to electronic structure ata obtaine at the CASPT2(2,2)/aug-cc-pVDZ level of theory. Interfragment (center of mass to center of mass) istances were sample from 250 pm to 800 pm, while the two angles escribing the relative position of both fragments were sample in steps of 15. The three Euler angles escribing the orientation of the methyl fragment were sample in steps of 30. The planar D 3h symmetry of the methyl fragment was use to reuce the require number of sampling points by a factor 6. Nevertheless, a total of 1,078,272 single point evaluations were performe. Corrections were ae in orer to properly account for the effect of the isproportionation channel on the ynamics. These corrections were obtaine from intrinsic reaction coorinate calculations an correct for the relaxation of the O H bon length an orientation as the methyl fragment approaches the hyroxyl group. Rate coefficients Rate coefficients for the channels with tight transition states were obtaine using conventional transition state theory: A B E(0K) BT BT Q = κ ( T) e (1) h Q Q 2

3 where Q is the partition function per unit volume. Internal moes were consiere as harmonic oscillators except for the rovibrational moes, which were treate as 1-D hinere rotors. The Ecart scheme was applie to obtain tunneling corrections. For the loose transition states, which are characterize by large interfragment istances, the harmonic oscillator approximation breas own. For these channels, the transition state moes are more accurately escribe by classical phase space integrals. To reuce the imensionality of those integrals, internal moes are consiere to behave aiabatically an to be completely ecouple from the transitional moes. This reuce imensional framewor has been implemente in the CROSSRATE coe an can be use for both statistical an ynamical calculations. Dynamical evaluations are conucte by running trajectories in the configuration space spanne by the 6 transitional moes. Each trajectory initiates from a given iviing surface an terminates when an energy constraint is met or when the trajectory crosses a user-efine bounary. Statistical theory for roaming We have recently evelope a statistical theory that quantifies the effect of roaming pathways on prouct branching fractions (Klippenstein et al. 2011). The essence of this scheme involves a ivision of the configuration space into istinct species. Recombination reactions are typically characterize by both a short an long range transition state an the volume between both iviing surfaces can be interprete as an intermeiate prouct. As a result, the configuration space for the CH 2 OH + CH 3 system can be ivie into 5 regions (see Figure 1). The inetic equations for the concentrations of species A, 1, 2, P 1 an P 2 can be written as: [ A] / t = ( A,1 + A,2) [ A] [ 1] / t = A,1[ A] + 2,1[ 2] ( 1,A + 1,2 + 1,P1 )[ 1] [ 2] / t = A,2[ A] + 1,2 [ 1] ( 2,A + 2,1 + 2,P2) [ 2] [ P1] / t = 1,P1 [ 1] [ P2] / t = [ 2] 2,P2 (2) with i,j the rate coefficient for transformation of species i to j. The steay-state assumption for intermeiates 1 an 2 yiels the following expression for the branching between isproportionation an recombination: Figure 1: CASPT2(2,2)/aug-cc-pVDZ potential energy (J mol -1 ) plot for the CH 2 OH + CH 3 system. The blac ashe lines represent the iviing surfaces separating the reactants CH 3 + CH 2 OH (A) from two long range intermeiates 1 an 2 an the two proucts, i.e. ethanol (P1) an CH 2 O + CH 4 (P2). The oxygen, carbon, an hyrogen atom of the CH 2 OH fragment efining the xy-plane are inicate in blac. 3

4 Figure 2: CASPT2(2,2)/cc-pVTZ potential energy (J mol -1 ) plot in spherical coorinates for the system CH 2 OH + CH 3. The epicte energies are the minimum energies obtaine for single point calculations at interfragment istances ranging from 250 to 1000 pm. Energies are relative to the CH 2 OH + CH 3 asymptote. The contour spacing is 1 J mol -1. θ escribes the position of the methyl fragment in the OCH plane (see Figure 1 for efinition). θ = 0 correspons with the methyl fragment being positione in the extension of the C O bon facing the oxygen atom. φ correspons with the out of plane motion. The angular epenent part of the iviing surface separating the two intermeiates (1 an 2 on Figure 1) is inicate by the ashe line. [ P2] / [ P1] = 2,P2 1,P1 1,2 ( 2,A + A,2 A,1 + 2,1 ( 1,A + + 2,P2 1,2 ) + + A,2 A,1 1,P1 ) 2,1 (3) The rate coefficients in equation (3) can be replace by the corresponing reactive fluxes or by the canonical partition function of the transition state within the microcanonical or canonical framewor, respectively. 3. Results an Discussion Potential energy surface an iviing surface In this wor, we focus on just the C C scission because breaing the C O or one of the C H bons in ethanol is at least 25 J mol -1 more highly activate. A preliminary scan was performe at the CASPT2(2,2)/cc-pVTZ level in orer to capture the characteristics of the potential energy surface of the CH 3 + CH 2 OH system. The results of this scan are presente in Figure 2. Three istinct wells are clearly visible. Two of them correspon with recombination channels: one channel above an one unerneath the CH 2 OH plane. These channels are locate at θ = 180 an φ = ± 60. The thir well (θ = -60 an φ = 0 ) correspons with the methyl fragment aligning with the O H bon. This van er Waals complex has an energy 8 J mol -1 below the issociation asymptote. The multiimensional nature of the stuie problem hampers the ivision of the configuration space into separate species. Base on the results presente in Figure 2, we opte for a iviing surface that is constructe from three intersecting planes. The iviing surface encompasses the van er Waals intermeiate an passes through most of the important riges separating the recombination channels from this intermeiate. Spheres, having the center of mass of the CH 2 OH fragment as their origin, were use to further ivie the configuration space into proucts, intermeiates an reactants. Stationary points The CASPT2(2,2)/CBS an CCSD(T)/CBS zero-point correcte energies of the various stationary points encountere on the CH 3 + CH 2 OH surface are presente in Table 1. The T1 iagnostics were monitore an the CCSD(T) energies are put in parentheses when this iagnostic suggests significant contributions of multi-reference effects. CASPT2 preicts a barrier for C C scission of J mol -1, which is 16 J mol -1 lower than obtaine with 4

5 Table 1: Zero point vibrational energy correcte stationary points energies for the CH 2 OH + CH 3 potential energy surface. The energies are expresse relative to the energy of the issociation asymptote. Stationary point CASPT2(2,2)/CBS CCSD(T)/CBS CASPT2(4,4 2,2)/cc-pVDZ a CH 3 + CH 2 OH CH 3 CH 2 OH vw b CH 3 CH 2 OH CH 4 + CH 2 O (tight) CH 3 CH 2 OH vw (roaming) vw CH 4 + CH 2 O -3.0 (-6.1) +1.4 CH 3 CH 2 OH CH 4 + HCOH a CASPT2(4,4 2,2) = effect of extening the active space from 2 electrons, 2 orbitals to 4 electrons, 4 orbitals b vw enotes van er Waals complex CCSD(T). Various sale points can be foun having an energy close to the issociation asymptote. Generally the CCSD(T)/CBS barriers are 10 J mol -1 lower than obtaine with CASPT2. For example, CASPT2 an CCSD(T) preict barriers for CH 3 CH 2 OH CH 4 + HCOH that lie respectively 1.5 an 12.3 J mol -1 uner the issociation asymptote. Using G2M(RCC2) Par et al. (2002) foun a barrier for this channel that is 13.4 J mol -1 uner the issociation asymptote, which supports the CCSD(T) results. The eviations are liely cause by the moest active space use. This is illustrate in the last column of Table 1 where the influence of an increase of the active space is stuie for a ouble zeta basis set. For CH 3 CH 2 OH CH 4 + HCOH, aition of the σ an σ* orbitals of the C H bon to the active space ecreases the barrier by 3 J mol -1. In contrast, for the roaming transition state, the van er Waals complex an the isproportionation transition state, the size of the active space has no significant effect on the results. In Figure 3 the optimize CASPT2 geometries are presente for the roaming transition state, the van er Waals complex an the isproportionation transition state. The imaginary frequency in the roaming sale point amounts to 136 cm -1 an correspons to an inversion moe of the methyl raical. Similar roaming transition states have been observe for alanes (Haring & Klippenstein 2010). Once the methyl fragment crosses the roaming sale point, it starts to interact with the hyroxyl group. This can be erive from the increasing O H bon length. The CH istance is 222 pm in the van er Waals complex an ecreases to 181 pm for the isproportionation sale point. The imaginary frequency corresponing with the hyrogen abstraction amounts to 404 cm -1. This hyrogen abstraction is strongly couple with rotation of the O H bon out of the OCH plane of the CH 2 OH fragment. This rotation, which is require for the σ* O H orbital to overlap with the ajacent p orbital of the unpaire electron, is most liely responsible for the observe sale point. Figure 3: CASPT2(2,2)/cc-pVTZ geometries for (A) the roaming transition state, (B) the intermeiate van er Waals complex an (C) the isproportionation transition state. Bon lengths are given in pm. Imaginary frequencies an corresponing isplacements are given for the transition states. 5

6 Table 2: Arrhenius parameters ( =AT n exp(-e/t)) for the various rate coefficients stuie in this wor. a Reaction A n E (1300K) Conventional transition state theory CH 3 CH 2 OH H 2 O + C 2 H CH 3 CH 2 OH CH 4 + HCOH CH 3 CH 2 OH CH 4 + CH 2 O (tight) Statistical Reuce Dimensional Framewor CH 3 CH 2 OH CH 4 + CH 2 O (roaming) Dynamical Reuce Dimensional Framewor CH 3 CH 2 OH CH 3 + CH 2 OH CH 3 + CH 2 OH CH 3 CH 2 OH CH 3 + CH 2 OH CH 4 + CH 2 O a The Arrhenius parameters are vali in the temperature range K. Rate coefficients are expresse in s -1 or cm 3 mol -1 s -1. Rate coefficients an branching ratios Arrhenius parameters an rate coefficients for the various reactions stuie in this wor are presente in Table 2. Rate coefficients are reporte at 1300 K as this temperature is roughly in the mile of the range where most experimental ata were obtaine. Generally, the presente values agree within a factor 2 of other ata reporte in the literature (Kiercherer et al. 2011, Sivaramarishnan et al. 2010, Wu et al. 2011). To obtain rate coefficients for the roaming channel, use was mae of the statistical framewor presente by Klippenstein et al. (2011). The branching ratio (CH 3 CH 2 OHCH 4 +CH 2 O)/(CH 3 CH 2 OHCH 3 +CH 2 OH) was foun to fluctuate aroun 2%. Only a moest temperature epenence was observe: with the branching ratio varying from 1.5% at 500 K to 2.5% at 1500 K. Multiplication of these branching ratios with the rate coefficient for C C scission, obtaine from statistical evaluations on the constructe potential energy surface, yiels the values presente in Table 2. Rate coefficients for C C scission an water elimination are at least one orer of magnitue larger an hence only minor contributions of roaming are expecte. As the rate coefficients for all irect reaction paths to methane are small, hyrogen abstraction reactions by methyl are expecte to be the main methane source. For the ynamical stuy, trajectories were initiate from a sphere positione at the center of mass of the CH 2 OH fragment with a raius of 500 pm. It was valiate that the results are inepenent of the chosen iameter of the sphere. The resulting Arrhenius parameters an rate coefficients for recombination r an isproportionation are shown in the two last rows of Table 2. The ratio / r is plotte in Figure 4 as function of temperature an compare with the preictions obtaine using equation (3). The isproportionation reaction is suppresse at lower temperatures as a large fraction of the methyl fragments that initially approach the hyroxyl group en up roaming towars the recombination channel instea of participating in the isproportionation reaction. This is attribute to fast roaming an the fact that a tight transition state region nees to be crosse for isproportionation to occur. At lower temperatures the agreement between the statistical framewor an trajectory calculations is striing. However, at higher temperatures the statistical approach tens to overestimate the branching ratio, probably ue to a moest ynamical biasing. It is further illustrate in Figure 4 that at higher temperatures equation (3) reuces to 2,P2 / 1,P1. Simulations For the simulations we opte to use the networ presente by Green an coworers that has recently been evelope to escribe the combustion an ecomposition of butanol isomers (Harper 2011). In this networ, most reactions relevant to the ecomposition of ethanol originate from the GRI-Mech3.0 networ an from the wor of Marinov (1999). We implemente our rate coefficients for C C scission, isproportionation, an roaming. Pressure epenencies for the scission reaction were taen from Sivaramarishnan et al. (2010). Simulations were performe with the CHEMKIN 4.0 pacage an the results of those simulations are presente in Figure 5 where they are compare with experimental ata recently presente by Kiercherer et al. (2011). It can be seen that the n-butanol networ with the moifie rate coefficients for ethanol accurately reprouces the experimental concentration profiles. 6

7 / r T / K Figure 4: Preicte branching ratio between isproportionation an recombination, / r, for CH 3 an CH 2 OH as function of the temperature: obtaine from equation (3), obtaine from trajectory calculations. Green an purple lines enote smooth fits to these ata. The ratio 2,P2 / 1,P1 (see Figure 1 for efinitions) at various temperatures is inicate with the full blac line. Notably, it was foun that roaming has only a minor contribution on the prouct istribution. Inclusion of roaming leas to only a minor acceleration of the ecomposition rate of ethanol, i.e. an increase of 3%. Yiels of methane an CO merely increase by 6 an 3%, respectively. It is observe in Figure 5 that the CH 4 yiel is still slightly unerestimate, while at the same time the preicte C 2 an H 2 O yiels are in the higher en of the experimental ata. In orer to match the CH 4 yiels, the rate coefficient for roaming nees to increase by a factor 30. This seems an unrealistically high value given the features of the potential energy surface. The iscrepancies between the moele an experimental CH 4 yiels are hence more liely ue to small uncertainties in other rate coefficients such as those for methyl abstraction reactions. 15 Concentration / 10-8 mol cm time / ms Figure 5: Concentration-time profiles uring shoc-tube experiments for the pyrolysis of ethanol at T = 1380 K, p = 1.1 bar an [CH 3 CH 2 OH] 0 = mol cm -3. Symbols represent experimental values: ethanol, H 2 O, C 2 H 4 + C 2 H 2, acetalehye, CH 4. Lines represent simulate values. The green an purple lines are nearly overlapping an so are ifficult to istinguish. 7

8 4. Conclusions The influence of roaming mechanisms on the pyrolysis of ethanol has been stuie. We focuse on C C bon scission as the bon issociation energy for this bon is at least 25 J mol -1 lower than that obtaine for the other bons in ethanol. Using multi-reference methos (CASPT2/aug-cc-pVDZ) a etaile potential energy surface was constructe that allows for the implementation of both statistical an ynamical simulations. A roaming transition state was ientifie with an energy of approximately 3 J mol -1 uner the issociation asymptote. Once this barrier has been crosse the methyl raical can stabilize in a van er Waals well before participating in isproportionation reactions with the CH 2 OH fragment. However, the relatively tight transition state for isproportionation from the van er Waals intermeiate hampers the irect conversion from ethanol to CH 4 + CH 2 O. A statistical evaluation shows that the branching ratio towars this prouct channel is limite to a few percent. The characteristics of the stuie potential energy surface reveal an interesting feature that might be universal for isproportionation reactions involving alcohols. For the reverse bimolecular reactions, the branching ratio between isproportionation an recombination tens to be strongly temperature epenent. At low temperatures (500 to 800 K) almost no successful trajectories towars isproportionation can be obtaine as methyl raicals easily roam towars the recombination channel. However, as temperatures increase up to 1000 K, the isproportionation channel tens to become active an branching ratios of more than 10% are obtaine. To our nowlege this is one of the first times that the effect of roaming on a bimolecular channel has been ocumente. Acnowlegements This wor is supporte by the Division of Chemical Sciences, Geosciences, an Biosciences, the Office of Basic Energy Science (BES) of the U.S. Department of Energy as part of the CEFRC through contract Number DE-SC References L. B. Haring an S. J. Klippenstein, Roaming Raical Pathways for the Decomposition of Alanes, J. Phys. Chem. Lett. 1 (2010) M. R. Harper, K. M. Van Geem, S. P. Pyl, G. B. Marin an W. H. Green, Comprehensive Reaction Mechanism for n-butanol Pyrolysis an Combustion, Combust. Flame 158 (2011) J. Kiercherer, T. Bentz, C. Hüllemann, K. Blumenstoc an M. Olzmann, Pyrolysis of Ethanol-Shoc-Tube/TOF- MS Stuy an Kinetic Moeling, 5 th European Combustion Meeting (2011). S. J. Klippenstein, Y. Georgievsii an L. B. Haring, Statistical Theory for the Kinetics an Dynamics of Roaming Reactions, J. Phys. Chem. A 115 (2011) J. Li, A. Kazaov an F. L. Dryer, Ethanol Pyrolysis Experiments in a Variable Pressure Flow Reactor, Int. J. Chem. Kinet. 33 (2001) N. M. Marinov, A Detaile Chemical Kinetic moel for High Temperature Ethanol Oxiation, Int. J. Chem. Kinet. 31 (1999) MOLPRO is a pacage of ab initio programs written by H.-J. Werner an P. J. Knowles (2010), with contributions from (a) C. Hampel, K. A. Peterson an H.-J. Werner, Chem. Phys. Lett. 190 (1992) 1-12, (b) P. Celani an H.-J. Werner, J. Chem. Phys. 112 (2000) , an (c) P. Celani an H.-J. Werner, J. Chem. Phys. 119 (2003) J. Par, R.S. Zhu an M.C. Lin, Thermal Decomposition of Ethanol. I. Ab Initio Molecular Orbital/Rice- Ramsperger-Kassel-Marcus Preiction of Rate Constant an Prouct Branching Ratios, J. Chem. Phys. 117 (2002) R. Sivaramarishnan, M.-C. Su, J. V. Michael, S. J. Klippenstein, L. B. Haring an B. Ruscic, Rate Constants for the Thermal Decomposition of Ethanol an Its Bimolecular Reactions with OH an D: Reflecte Shoc Tube an Theoretical Stuies, J. Phys. Chem. A 114 (2010) R. Sivaramarishnan, J. V. Michael, L. B. Haring an S. J. Klippenstein, Shoc Tube Explorations of Roaming Raical Mechanisms: The Decompositions of Isobutane an Neopentane, J. Phys. Chem. A 116 (2012) C.-W. Wu, H. Matsui, N.-S. Wang an M. C. Lin, Shoc Tube Stuy on the Thermal Decomposition of Ethanol, J. Phys. Chem. A 115 (2011)