Understanding Trends in Autoignition of Biofuels: Homologous Series

Article pubs.acs.org/JPCA

Understanding Trends in Autoignition of Biofuels: Homologous Series of Oxygenated C5 Molecules Lintao Bu, Peter N. Ciesielski, David J. Robichaud, Seonah Kim, Robert L. McCormick, Thomas D. Foust, and Mark R. Nimlos* National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401, United States S Supporting Information *

ABSTRACT: Oxygenated biofuels provide a renewable, domestic source of energy that can enable adoption of advanced, highefficiency internal combustion engines, such as those based on homogeneously charged compression ignition (HCCI). Of key importance to such engines is the cetane number (CN) of the fuel, which is determined by the autoignition of the fuel under compression at relatively low temperatures (550−800 K). For the plethora of oxygenated biofuels possible, it is desirable to know the ignition delay times and the CN of these fuels to help guide conversion strategies so as to focus efforts on the most desirable fuels. For alkanes, the chemical pathways leading to radical chain-branching reactions giving rise to low-temperature autoignition are well-known and are highly coincident with the buildup of reactive radicals such as OH. Key in the mechanisms leading to chain branching are the addition of molecular oxygen to alkyl radicals and the rearrangement and dissociation of the resulting peroxy radials. Prediction of the temperature and pressure dependence of reactions that lead to the buildup of reactive radicals requires a detailed understanding of the potential energy surfaces (PESs) of these reactions. In this study, we used quantum mechanical modeling to systematically compare the effects of oxygen functionalities on these PESs and associated kinetics so as to understand how they affect experimental trends in autoignition and CN. The molecules studied here include pentane, pentanol, pentanal, 2-heptanone, methylpentyl ether, methyl hexanoate, and pentyl acetate. All have a saturated five-carbon alkyl chain with an oxygen functional group attached to the terminal carbon atom. The results of our systematic comparison may be summarized as follows: (1) Oxygen functionalities activate C−H bonds by lowering the bond dissociation energy (BDE) relative to alkanes. (2) The R−OO bonds in peroxy radicals adjacent to carbonyl groups are weaker than corresponding alkyl systems, leading to dissociation of ROO• radicals and reducing reactivity and hence CN. (3) Hydrogen atom transfer in peroxy radicals is important in autoignition, and low barriers for ethers and aldehydes lead to high CN. (4) Peroxy radicals formed from alcohols have low barriers to form aldehydes, which reduce the reactivity of the alkyl radical. These findings for the formation and reaction of alkyl radicals with molecular oxygen explain the trend in CN for these common biofuel functional groups.

1. INTRODUCTION The historic drivers for the development of biofuels in the United States have been to reduce dependence on imported petroleum for transportation fuels and the desire to decrease greenhouse gas emissions. Biofuels deployment in this context has been focused on a petroleum displacement strategy that involves meeting volume targets such as those defined in the Renewable Fuel Standard,1 which employs biofuels as supplements to petroleum-based fuels in the fuel supply. The most prevalent example of this approach is E10 (10% ethanol) in motor gasoline. An approach to achieving even greater benefit is to develop biofuels with advantageous properties allowing the design of higher-efficiency, lower-emitting engines.2 © XXXX American Chemical Society

A number of studies have identified promising characteristics of biofuels such as the high research octane number (RON) blending aspect of ethanol for spark ignition engines3,4 or the soot reduction potential of tripropylene-glycol monomethyl ether in compression ignition (CI) engines.5 In both cases, oxygen functional groups are responsible for critical fuel properties. Using biomass or sugar as a feedstock opens the potential for a broad range of oxygen functionality to be considered in fuels.6,7 Autoignition is a critical fuel property for Received: April 29, 2017 Revised: June 29, 2017 Published: July 5, 2017 A

DOI: 10.1021/acs.jpca.7b04000 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

molecular oxygen to form •OOQOOH, which abstracts a second hydrogen internally, leading to the formation of a ketohydroperoxide and an OH radical. As temperatures increase, the O−O bond in the ketohydroperoxide breaks, producing two radical species. The overall reaction of OOQOOH therefore produces three radical species, two OH and an oxidized hydrocarbon radical, and is the primary chainbranching process in low-temperature autoignition. For the reversible oxygen addition reactions, the forward reaction is favored by higher pressure, and the reverse reaction is favored at higher temperature. As temperatures increase above about 850 K, the reversibility of these reactions begins to diminish low-temperature autoignition. Isoalkanes have less opportunity to undergo low-temperature autoignition, especially if highly branched, because they possess fewer methylene groups. For example, 2,2,4-trimethylpentane (isooctane) has very low reactivity and defines RON = 100 on the octane number scale. Small alkanes such as methane or ethane are also unable to undergo this reaction sequence. Ethane is estimated to have a RON of 11550 yet is a gas under ambient conditions, making it impossible to use in gasoline. Addition of an OH group to form ethanol slightly reduces RON to 109, which makes the fuel more reactive but creates a liquid that can be blended with conventional gasoline. However, other small molecules can be highly reactive, such as dimethyl ether with CN over 55. In this molecule, weak C− H bonds lead to peroxyradical formation and a similar reaction sequence to that shown above.51 Aromatic molecules cannot undergo this low-temperature reaction sequence and therefore have low reactivity (high RON). Several side reactions compete with the chain-branching pathway and can reduce the rate of autoignition. The ROO• radical can decompose to an olefin and HO2 radical, which is much less reactive than OH or alkoxy radicals, and results in chain termination reactions such as self-reaction, HO2 + HO2 → H2O2 + O2, for instance. The QOOH radical can also undergo a chain propagation reaction to produce a single OH radical, accompanied by the formation of an olefin and an aldehyde or formation of a cyclic ether. High cetane fuels have a propensity toward branching reactions, where high octane fuels are directed toward chain propagation and termination reactions. Though these reaction pathways have been well studied for hydrocarbons, there is no systematic comparison between different oxygenates found in biofuels, which elucidates the effect of oxygen functional groups on the reaction energies and activation barriers for these reactions. There are prior studies of the impact of oxygen functionality on alkyl chain autoignition reactivity. Heufer and co-workers studied the autoignition chemistry of 1-pentanol and demonstrated that the primary reaction paths involve hydrogen abstraction from the C1 and C4 carbons.52 However, reaction at the C1 carbon is a chain termination path leading to formation of pentanal and HO2 radical, while reaction at the C4 carbon leads to QOOH formation and continuation of the chain-branching process. Pentanal autoignition has been examined by Pelucchi and co-workers.21 Hydrogen abstraction occurs primarily at the C1 site, and the radical formed can decompose via chain-propagating steps or preferentially reacts with oxygen, ultimately forming QOOH and entering the chain-branching process. Recently, a very thorough review explored the chemical rationale for octane number in oxygenated fuel molecules53 by gathering experimental and computational bond energies and reaction barriers.

engine performance that is quantified using the engineering metrics RON or cetane number (CN). Experimental examination of autoignition for all of the different possible oxygenated biofuel molecules across the gamut of different autoignition modes for different engine options would be extremely time- and resource-intensive. Additionally, such an approach would not lead to new fundamental insights into the effect of oxygen functionality on autoignition properties. Numerous chemical kinetic modeling and experimental studies have been conducted to investigate the autoignition properties of biofuel model compounds, including C4−C6 alcohols,8−18 C3−C5 aldehydes,19−22 ketones,23,24 esters,25−30 and ethers.24,31−33 However, most of the rate constants used in these kinetic models are empirically determined and therefore may not reflect reliable reaction energy barriers such as those obtained from QM calculations. Some QM studies have also been conducted to explore the activation mechanisms of chosen biofuel model compounds, such as ethanol,34,35 butanone,36,37 methyl butanoate,38−40 dimethyl ether,41,42 and diethyl ether.43,44 The length of the alky chain only varies from C2 to C3 in these studies, and hydrogen transfer reactions may require the abstraction of a hydrogen atom from a primary carbon, resulting in a higher energy barrier. This work examines the autoignition properties of oxygentated molecules by specifically investigating the autoignition pathways opened with oxygen functional groups for a homologous series of pentane derivatives. The predominant pathways thought to be important in low-temperature autoignition of n-pentane are shown in Figure 1.45 n-Alkanes with

Figure 1. Schematic mechanisms of autoignition chemistry of pentane.

five or more carbon atoms are highly reactive because the interior methylene C−H bonds are relatively weak and can undergo hydrogen abstraction by molecular oxygen.46 The alkyl radical product combines with molecular oxygen to form a peroxy radical, ROO•, in a reversible reaction. This radical undergoes intramolecular hydrogen transfer via formation of a 5−8-membered ring transition state (depending on the structure of the molecule) to form a hydroperoxy alkyl radical, QOOH.47−49 This reversible reaction adds an additional B


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number indicates the position on the pentyl chain of the carbon atom starting at the carbon of the functional group. For pentane, carbon atom number 1 is one of the primary carbon atoms. For pentanol, pentanal, pentyl acetate, and the ethers, carbon atom number one is the carbon on the pentyl chain that is bonded to the oxygen functional group. For pentanone and methyl hexanoate, C1 is the carbon atom adjacent to the carbonyl carbon. For the ethers, ketones, and esters, the carbon atoms on the side opposite the pentyl groups are given negative numbers. QM Calculations. The G4 compound quantum mechanical method was used to calculate energies of all species in this study, which is based on geometries and vibrational frequencies calculated using DFT with B3LYP/6-31g(2df,p).58 The reported accuracy of the G4 technique was estimated by a comparison of calculated energies to experimental energies for the 454 species in the G3/05 test set, which showed that the average absolute deviation was 0.83 kcal mol−1. The initial geometries of stationary points and transition states in the pentane molecule were adopted from Asatryan and Bozzelli.45 All of the transition states were characterized as having only one negative frequency and further confirmed by conducting intrinsic reaction coordinate (IRC) calculations using B3LYP/ 6-31g(2df,p) to ensure that they are connected to the reactants and the products. We have used the trans−trans conformational structure for all molecules in this study, as shown for pentane in Figure S1 in the Supporting Information. The conformations of the npentane molecule have been studied using both Raman spectroscopy59 and ab initio calculations.60 The Raman spectroscopy study demonstrated that the trans−trans conformation is more stable than the trans−gauche or gauche(+)−gauche(+) conformation with an enthalpy difference of 0.6 or 0.9 kcal mol−1, respectively.59 The ab initio calculations via the MP2 level of theory reported that the energy difference between the trans−trans conformation and trans−gauche or gauche(+)−gauche(+) conformation is 0.7 or 1.1 kcal mol−1, respectively.60 Rate Constant Determination. Rate constants were typically determined using transition state theory (TST), shown in eq 1, where kB is Boltzmann’s constant, h is Planck’s constant, T is the temperature, QTS is the partition function for the transition state, QReact is the partition function for the reactant, ΔE0 is the energy difference between the transition state and the reactant including the zero-point energy, and R is the gas constant. The partition functions were determined with the rigid rotor and harmonic oscillator approximation. No contribution for hindered rotors was used, nor were contributions from tunneling. Hindered rotor calculations47 have shown that an additive correction of 1−2 cal mol−1 K−1 per rotor relative to the harmonic oscillator approximation will result. This will have a small impact on total calculated entropies, which are typically >90 cal mol−1 K−1, and hindered rotors should have an impact of up to a factor of 10 on the rate constants. For most of the calculations here, many of the rotors will cancel when calculating rate constants. The Wigner estimate for tunneling61 shows that a correction factor of 2 can be obtained. Both of these factors will, to a certain extent, cancel out when comparing reaction rates of different species in the homologous series, but they will be included in a subsequent publication that focuses on kinetics. That publication will also include thermodynamic values for these molecules. The TST rate constants were calculated for

In this study, we use quantum mechanical molecular modeling to systematically explore the effects of oxygen functionalities that are common in biofuels in order to understand how they lead to differences in CN. We subsequently consider the effects of chemical activation by using quantum Rice−Ramsperger−Kassel (QRRK)54−56 to investigate the pressure dependence of the unimolecular decomposition of the ROO• radicals. Earlier work showed that the pressure dependence was not important for alkanes at pressures relevant to engine combustion (>10 atm).49 Here we explore this dependence for oxygenates. For this comparison, we have considered six oxygenated groups attached to a C5 alkyl chain, as shown in Table 1. C5 molecules were chosen Table 1. List of Model Compounds Studied in This Work

a

CNs are taken from a recent compilation.57 bThe CN of methylpentyl ether is estimated based upon other ethers in the compilation.

because these constitute the smallest chain length for alkanes found at significant levels in gasoline. This list includes alkanes, R, for reference to hydrocarbon fuels, alcohols, ROH, aldehydes, RO, ketones, RCOCH3, ethers, ROCH3 and esters, RCO2CH3, and ROCOCH3. These molecules all have five carbon atoms on the alkyl chain with a hydrogen atom that is available for abstraction to form a radical. In this initial study, we consider the addition of the first molecular oxygen to the alkyl radical resulting from H atom abstraction from these oxygenates. In a follow-up publication, we compare the reactions that are important with the addition of the second molecular oxygen, that is, QOOH + O2 → OOQOOH → ?. Our study is differentiated from a recent review53 in that we use a single computational level of theory, G4, to systematically compare the competing oxidation channels for oxygenates with similar alkyl chains. However, our results are consistent with this earlier study, providing a level of validation to our approach.

2. METHODS Model Compounds. The molecules studied in this work are listed in Table 1. The abbreviation names of the chemical species were adopted from Asatryan and Bozzelli45 and are shown in Table S1 in the Supporting Information. Specifically, J indicates a radical center, Q stands for an OOH group, and QJ represents an OO• group. For example, PN1J is the 1-pentyl radical, PN1QJ is the 1-pentylperoxy radical (ROO•), and PN1Q3J is the 1-pent-3-yl-hydroperoxide (QOOH). The C


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The Journal of Physical Chemistry A Table 2. BDEs (kcal mol−1) for C−Ha pentane (PN) pentanol (POH) pentanal (PAL) heptanone (HON) methylpentyl ether (MPO) methylhexanoate (MH) pentylacetate (PA) average (SD)b

BDE BDE BDE BDE BDE BDE BDE BDE

C1

C2

C3

C4

C5

C-1

100.3 93.3 87.5 90.8 93.3 91.6 95.8 92.1 (2.8)

97.5 98.4 88.5 96.7 98.1 96.8 97.7 97.5 (0.8)c

97.8 97.4 97.0 96.8 97.1 96.5 96.7 96.9 (0.3)

− 97.2 97.5 96.6 96.9 96.3 96.4 96.8 (0.5)

− 100.0 100.0 99.1 99.3 98.8 98.9 99.4 (0.5)

94.1 94.3 97.1 96.0 95.4 (1.4)

a

Calculated using G4 theory. The values in bold are for the radicals studied in the present work. bValues are averaged over the oxygenates; SD is the standard deviation. cThe values for pentanal were not included in this average or standard deviation.

temperatures from 300 to 1500 K and fitted to an Arrhenius formula to obtain the activation energy, Ea and the preexponential factor, A. The rate constants for the addition of O2 to the radicals, kadd, were assumed to be the same as the measured rate constant62 for O2 + ethyl radicals, A = 4.40 × 1012 cm3 mol−1 s−1 and Ea = 0.0 kcal mol−1. The reverse rate constant was determined by calculating the equilibrium constant, Keq, and ratio kdisc = kadd/Keq, where eq 3 was used for the equilibrium constant. QROO, QR, and QO2 are the partition functions for the peroxy radical, the alkyl radical and molecular oxygen, and ΔE0 is the energy difference between the product and the reactants. kTST =

kBT QTS −ΔE0 / RT e h Q React

k = Ae−Ea

Keq =

d[P] = kp(T , P)[R][R′] dt

where R and R′ are reactants, Ai is stabilized adduct, and P is product, ki and kp are rate constants dependent on temperature, pressure, and collisions. The master equation is defined by balancing the flux of each species into and out of an energy level q f iq +

Q RQ O

p

∑ kjq,i + ω) (6)

j

f qi

where i and j denote isomers, p denotes product, is the rate constant via the reactant channel, kqi,j is the isomerization rate from isomer j to isomer i, nqj is the population of isomer j, Pq,r i is the probability of a collision that causes isomer i to change its energy level from r to q, and dqp,i is the dissociation rate constant from isomer i to product p. ω is the frequency of collisions between the adduct and bath

(1)

(3)

ω = [M ]NAπσ 2 Ω[2,2](T )

QRRK. The pressure dependence of the reaction of O2 with alkyl radicals is critical in autoignition because the chemically activated ROO• radical can either undergo unimolecular reaction or be quenched by collisions with other gas molecules. The rates of quenching will be dependent on the pressure. The calculations of the temperature- and pressure-dependent rate constants k(T,P) closely follow the strategies of Dean56 and Bozzelli45 and are conducted using ChemDis code based on QRRK theory with master equation analysis. The highpressure-limiting rate constants are calculated using TST, as discussed above for both the bimolecular addition reactions and unimolecular isomerization and thermal dissociation reactions. A reduced set of three apparent vibrational frequencies derived from heat capacity data is used to calculate the molecular density of states ρ(E). The modified strong collision model was used to calculate the collisional deactivation of the energized radicals. The average energy transferred in a deactivating collision with N2 as the third body is 0.440 kcal mol−1. The Lennard-Jones parameters, σ and ε, used in this work are 4.94 Å and 450.0 K for the C5 molecules and 3.62 Å and 97.5 K for the collider N2. The overall rate constants for isomerization and products are defined as d[A i] = ki(T , P)[R][R′] dt

r

= niq(∑ dpq, i +

e−ΔE0 / RT

2

∑ kiq,jnjq + ω ∑ Piq,rnir j

(2)

Q ROO

(5)

8kT πμ

(7)

where NA is Avogadro’s number, σ is the average of that of the complex and collider, μ is the reduced mass, and Ω[2,2](T) is defined as ⎛ kT ⎞−c1 Ω[2,2](T ) = a1⎜ ⎟ + a 2e−c2kT / ε + a3e−c3kT / ε ⎝ ε ⎠

(8)

where ε is the geometric mean of that of a complex and collider and a1, a2, a3, c1, c2, and c3 are fitted parameters. The overall rate constant for product channel p is then calculated by

kp(T , P) =

∑ dpq,iniq q

A more detailed description of this analysis method can be found in refs 54−56.

3. RESULTS AND DISCUSSION Hydrogen Atom Abstraction. Abstraction of a hydrogen atom is the first step in the chemistry leading to autoignition, and we have calculated the bond dissociation enthalpies (BDEs) and attempted to calculate the barriers for hydrogen atom abstraction by molecular oxygen in order to identify trends in oxygenates. Table 2 compares all of the C−H BDEs for the molecules in this study. BDEs were determined by calculating the room-temperature enthalpies for the model

(4)

and D


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oxygenate. For the other oxygenates, the C−O bond is shorter in the radical. This effect is shown in Table S2 in the Supporting Information. Molecular orbitals of the HOMO confirm the resonance stabilization as shown for methylpentyl ether and heptanone in Figures S2 and S3 in the Supporting Information. Formation of ROO• Radical. Addition of molecular oxygen to alkyl radicals to form peroxyradicals, ROO•, is an exothermic reaction, and the R−OO BDE is critical to autoignition. The R−OO• BDEs for C1 (and C2 for pentanal) and C3 are compared in Table 3. The C3 BDEs are similar to

compounds and the corresponding radicals. The results from these calculations point to more facile abstraction of the hydrogen atoms adjacent to the functional groups than to the other hydrogen atoms or the hydrogen atoms on pentane. The C−H BDEs for the C1 atoms of the oxygenates and the C2 atom of pentanal are between 88.5 and 95.8 kcal mol−1, while the BDEs for the other carbon atoms are about 97 kcal mol−1 for secondary carbon atoms in the rest of the molecules or 100 kcal mol−1 for primary carbon atoms, as shown by the averages in Table 2. Note that the C2−C4 C−H bonds for heptanone and methylhexanoate and the C3 and C4 C−H bonds of pethyl acetate are lower than the other C−H bonds. It is not clear if these are systematic differences or if they are due to random variations in the calculations. Likewise, we have not determined if the variations in the C5 C−H bond energies are systematic or random. These values are within the experimental and computational uncertainty of experimental values for ethane and propane, DH(C2H5−H) = 101.4 ± 0.4 kcal mol−1 and DH((CH3)2CH−H) = 98.6 kcal mol−1.63 The BDEs for the carbon atoms adjacent to the functional groups (C1) are similar to experimental measurements for methanol (96.1 ± 0.2 kcal mol−1), formaldehyde (88.144 ± 0.008 kcal mol−1), and acetaldehyde (89.4 ± 0.3 kcal mol−1).64 The accuracy of these barrier heights was difficult to determine because there have been very few studies of hydrogen atom abstraction by O2. There has been some experimental65 and theoretical (CCSDT and QCISD)66 work to determined the barrier for hydrogen abstraction from methane, which reported a barrier of 56 kcal mol−1 with a complex binding energy of about 4 kcal mol−1. The low C−H BDE for all of the oxygenates relative to pentane is due to stabilization of the resulting radical, as portrayed in Figure 2. For the carbonyl compounds, resonance

Table 3. R−OO BDEs this worka

R

37.5 (C2) 39.6 (C1)

37.2 (C3) 36.9 (C3)

PAL

35.5 22.2 27.6 36.3 26.6 37.0

35.4 37.5 36.8 37.2 36.5

HON MPO MH PA a

literature

PN POH

(C1) (C2) (C1) (C1) (C1) (C1)

(C3) (C3) (C3) (C3) (C3)

36.9 37.4 33.5 22.6

(n-C5H11)67 (CH3CHOH)35 (CH2CH2OH)68 (CH3CHCHO)69

25.0 (CH2C(O)CH3)70 33.8 (CH3OCH2)71

Calculated using G4 theory.

those for pentane, but some of the C1 and C2 BDEs of the oxygenates are different. The diagram in Figure 3 schematically

Figure 3. Diagram showing the effect of oxygen functional groups on the R−OO BDE. Figure 2. Diagram showing the effect of radical stabilization on the C− H BDE.

shows the observed trends. The same radical stabilization is operative as that for C−H BDEs, but when the peroxy group is adjacent to the oxygen atom, as in alcohols, ethers, aldehyde, and one side of esters, the electron withdrawing of the oxygenate stabilizes the peroxy radical, ROO•. The oxygen functional group withdraws charge from the C1 atom, which stabilizes the negatively charged peroxy radical group. Thus, for the C1 atoms on the carbonyls, and C2 on pentanal, the R− OO BDEs are lower than those of pentane, while they are of similar magnitude as those for the other oxygenates. Our calculated values for R−OO BDEs are in good agreement with previously published values calculated for similar molecules, as shown in Table 3.

structures lead to delocalization of the radical at the C1 position, C2 for pentanal, over the CO group. Thus, pentanal at C2 and heptanone and methyl hexanoate have weak C−H BDEs. For those molecules with a singly bonded oxygen atom and C1 of pentanal, the radical is stabilized by a partial π bond formation of the radical and a lone pair on the oxygen atom. This stabilization is not as strong as that due to delocalization with the carbonyls, except for pentanal. For the carbonyls, this stabilization of the radical leads to shorter C−C bond lengths adjacent to the carbonyl groups in the radicals relative to the E


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The Journal of Physical Chemistry A Reactions of ROO•. The reactions of peroxy radicals, ROO•, are critical during autoignition. We have systematically compared the potential energy surfaces for these reactions with those for pentane. Figure 4 shows a schematic of the important

of these barriers is largely determined by the ring strain47,48 in the transition state and the C−H BDE of the hydrogen being transferred. In general, the 6C TS and 7C TS are lower in energy than the 5C TS due to reduced ring strain. These transition states are also typically lower than the TS for olefin formation and for redissociation to give R• + O2. For oxygenates with an adjacent methyl group, heptanone, methylpentyl ether, methyl hexanoate, and pentyl acetate, abstraction from these methyl groups by a 6C or 7C TS is possible. Notably, because of low R−OO BDEs, the carbonyl peroxy radicals, PAL2QJ, HON1QJ, and MH1QJ, all have low barriers to dissociation, and this reaction competes with QOOH formation, increasing ignition delay and reducing CN. For pentanol, the reaction barrier for pentanal formation, rxn 1, is 14.1 kcal mol−1, and this reaction reduces QOOH formation and CN. This is consistent with values obtained for other alcohols.18,35 For the peroxy radicals located on C1 of pentanal, PAL1QJ, and methylpentyl ether, MPO1QJ, the barriers to QOOH are lower than those of the other molecules. In addition, MPO1QJ has a low barrier for abstracting a hydrogen atom across the ether group, from the methyl group. These low barriers help account for the high CNs for pentanal and methylpentyl ether. For hydrogen transfer across functional groups, the barriers for ketones and esters are higher because of strain in the transition state created by the carbonyl group. The C−C−C bond angle shown in Figure 6 for the peroxy radical is an average of 113.2° with a standard deviation of 0.6° for the 6C TSs along the alkyl chain, but for the ketone, because of the sp2 hybridization of the center carbon, the bond angle is 119° across the carbonyl group. For the transition states, the angle is an average of 112.0° with a standard deviation of 0.7° along the alkyl chain but 114.1° for the transition state across the carbonyl group. The angle change between the peroxy radical and the transition state is only about 1° for transfers along the alkyl group but over 5° across the ketone. This larger change in the bond angle puts greater strain on the transition state and increases the reaction barrier. The high barriers for hydrogen transfer across the esters, a 7C TS, is due to the even more significant changes of the angle centered on the carbonyl carbon atom. The angles shown in Figure 7 for the transition states for the esters dramatically changed by ∼8−10° relative to the ROO• reactant. This as compared to an average change of about 1° for the sevencentered hydrogen transfers along the alkyl groups. Additionally, the carbonyl group influences the planarity of the sevenmembered ring significantly. As shown in Figure 8, the atoms forming the 7C TS are nearly in the same plane for the TS across the functional group. On the contrary, the atoms are outof-plane for the TS along the alkyl chain. These results demonstrate that the carbonyl functional group can influence the geometry of the TS considerably, resulting in increased ring strain and thus a higher energy barrier. Reaction of QOOH. The unimolecular reactions of QOOH compete with addition of O2 to form •OOQOOH and include hydrogen transfer to re-form ROO•, addition/OH elimination to form cyclic ethers, or β-elimination to form an olefin and an aldehyde. The transition states for these reactions for pentane are shown in Figure S11, and the barriers are collected in Table 5, and for the most part, the barriers are similar. As with H atom transfer reactions to form QOOH, the barrier to re-form ROO• by hydrogen atom transfer from the α-C radical (PN2Q3J) is higher than that for the β- and γ-C radicals due

Figure 4. Schematic of the reaction products of 2-pentyl radical plus O2.

reaction pathways for pentane, as explored by Asatryan and Bozzelli.45 This reaction scheme will serve as a framework for describing the reaction sequences for all of the oxygenates discussed here, and similar schematics for the oxygenates are collected in the Supporting Information (Figures S4−S10). We have used G4 to calculate the minimized structures (with trans−trans conformations) for the reactions, products, and transition states for all of these reactions. The PESs for the oxygenates are compared to pentane in Figure 5, which serves as a basis for discussions about the effect on autoignition. Our G4 energies for the reaction of 2-pentyl radical compares favorably with earlier CBS calculations,45 as shown in Table S3 in the Supporting Information. The PESs shown in Figure 5 are for radicals formed by abstraction of a hydrogen atom from C1 for all oxygenates and C2 for pentanal. As discussed above, these hydrogen atoms are most susceptible to abstraction. Radicals produced by abstraction from the other carbon atoms in the oxygenates should have similar PESs as that shown for pentane, PN2J. Addition of molecular oxygen to the alkyl radical, R•, results in the formation of the peroxy radical, ROO•, which can typically rearrange to hydroperoxy radicals (QOOH), lose a HO2 radical to form an olefin, or dissociate to re-form R• and O2. For pentanol, there is an additional HO2 loss mechanism leading to pentanal (rxn 1). A competition between these reaction pathways is critical to the formation of QOOH, which ultimately combines with O2 to form •OOQOOH, which is essential to the radical branching reactions for autoignition.

The energy barriers for the reactions of ROO• are collected in Table 4, and the formation of the different QOOH species listed is identified by the transition states. The five-centered transition state (5C TS) involves hydrogen transfer from the adjacent, α carbon atom, while the 6C TS and 7C TS involve hydrogen transfer from the β and γ carbon atoms. The height F


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Figure 5. Potential energy surfaces of pentane and oxygenates considered here as determined using G4, with relative energies including the zeropoint energy. The products are shown in the schematics in Figures 4 and S4−S10.

shows, reaction of the α-C hydroperoxy radical (QOOH) to reform ROO• typically has a higher barrier than formation of the cyclic ethers or olefins. However, because formation of this radical from ROO• has a higher barrier than that for the other QOOH radicals, this is not likely to impact CN. For the β- and γ-C hydroperoxy radicals, the barriers to re-form ROO• are typically lower than those for the other decomposition pathways. As a result, an equilibrium will be established between ROO• and QOOH and autoignition will be determined by competition between the reaction of QOOH

to the ring strain in the transition state. Interestingly, the barriers for forming cyclic ethers from QOOH do not seem to follow this same trend. The α-C hydroperoxy radical forms a three-ring cyclic ether, oxirane, and has the lowest energy barrier, while forming the four-ring ether, oxetane, from the βC peroxy radical has the highest barrier and forming the fivering ether, oxolane, from the γ-C peroxy radical has a barrier height in the middle. This trend was observed earlier72,73 and is due to the stability of the transition state of the 3C TS compared to the reactant and its “early” nature.74 As Table 5 G


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The Journal of Physical Chemistry A Table 4. Energy Barriers (kcal mol−1) for the Reactions of ROO•a product ROO• → QOOH

HO2 R• + O2e

PN2J

POH1J

PAL1J

PAL2J

HON1J

MPO1J

MH1J

PA1J

5C TSb

34.6

34.7

25.1

32.5

31.0

33.9

32.7

6C TS 7C TS C-1 6C TS C-1 7C TS olefin other

22.8 25.8

23.9 23.4

20.7 18.6

19.3 (C1) 31.6 (C3) 23.2 25.3

22.2 21.1 29.0

20.8 19.5 19.4

23.2 22.2

23.0 21.4

31.1

32.5c 14.1 39.6

40.9d

25.5

33.0

32.9

32.3 30.4

31.5 31.5

35.5

22.2

27.6

36.1

26.6

37.0

37.5

a

Energy barriers include the zero-point energy. bC refers to the number of centers in the transition state. cThe olefin from 1-pentanol is an enol. dA ketene is formed from the PAL1QJ radical. eEnergy barriers for reaction to re-form R• + O2 are the reaction energies.

Figure 6. C−C−C bond angle in the peroxy radical and the 6C TS leading to hydroperoxide formation.

Figure 8. Geometry of the transition state for H-transfer via the sevencentered ring in methyl hexanoate across the functional group (A) and along the alkyl group (B).

with O2 and the formation of cyclic ethers. The other reaction pathways for QOOH radicals have high barriers. QRRK and Kinetic Analysis of R• + O2. The pressure dependence for this reaction for all molecules was investigated using QRRK using reaction schemes similar to that shown in Figure 4. (Reaction schemes for the other molecules are shown in the Supporting Information.) These calculations demonstrated that the reaction products have generally reached the high-pressure limit at 10 atm, which suggests that for pressures relevant to CI engines (compression ratios > 10) the products are invariant to pressure. Furthermore, with pressure stabilization of the adduct, ROO• is generally the dominant product from addition of O2 to the radical. The exception to this is pentanol, where the exit channel to pentanal formation has a low enough barrier that the rate is orders of magnitude larger than that of ROO• formation and the branching ratio between these channels continues to change with increasing pressure. Figure 9 shows an example of the pressure dependence of the rate constants for the reaction of 2-pentyl radical (PN2J) with O2 compared to hydroxypentyl radical (POH1J) from 1-pentanol. The figure shows that for pentyl radical, the pressure asymptote is reached at about 10 atm, while for hydroxypentyl radical, the rate constant for ROO• formation continues to grow with pressure as stabilization increases.

Figure 7. Schematic for important bond angles in the peroxy radical and the 7C TS leading to hydrogen transfer across the ester group. H


Article

The Journal of Physical Chemistry A Table 5. Barriers for the Reaction of QOOH in kcal mol−1 α-C radical PN C2 POH C1 PAL C1 PAL C2 HON C1 MPO C1 MH C1 PA C1 a

β-C radical

γ-C radical

ROOa

CYCb

HO2c

ROOa

CYCb

β-eld

ROOa

CYCb

19.7 19.7 19.1 19.7 22.0 19.9 19.2 19.4 19.5

11.9 6.4 16.2 26.2 15.2 8.7 12.0 11.2 12.9

16.3 17.6 36.0 28.2 15.7 15.9 20.1 13.6 20.7

9.1 11.6 13.0 13.4

19.9 14.7 16.6 18.5

26.9 33.4 28.8 22.2

8.6 9.0 11.1

15.0 10.2 13.8

8.5 8.6 8.2 9.0

17.7 17.0 14.8 15.7

20.5 29.1 29.3 35.6

8.0 8.3 7.8 8.3

13.7 13.6 10.9 11.8

across O ROOa

CYCb

20.4 11.3 12.2 22.1

29.7 27.3 11.6 28.1

Barrier for QOOH → ROO•. bBarrier for QOOH → cyclic ether + OH. cBarrier for QOOH → olefin + HO2. dBarrier for beta elimination.

Figure 10. Calculated rate constants for product formation from the unimolecular decomposition of PN2QJ.

atures, the rate constant for decomposition to R• + O2 is lower but still significant. Decomposition of ROO• to the olefin + HO2 (chain termination) or of QOOH (C4) to the cyclic olefin + OH (chain propagation) was much less significant with branching ratios less than 4 and 1%. These results are consistent with the PES for 2-pentyl radical, where the barrier for QOOH (C4) is smaller than the barrier for olefin formation and the exit barrier for QOOH (C4) going to the cyclic ether is higher than the entrance barrier. The barriers for formation of C3 and C5 QOOH radicals are higher than that for the C4 QOOH radical, and the branching ratios for these pathways are less than 2%, which is also consistent with the PES. The other peroxy radicals studied here appear to have two types of behavior with respect to the unimolecular decomposition. For those carbonyl molecules with a radical in the beta position relative to the carbonyl group, the reaction to R• + O2 is typically faster than the reaction to QOOH or the olefin product. As mentioned above, this is due to the low R−OO BDE. As a result, the dominant reaction of the ROO• peroxy radical is dissociation to regenerate the radical R• and O2. Figure 11B shows a plot of the rate constants for the products from the decomposition of the HON1QJ radical. These results show that the R• + O2 reaction is dominant and the rates for QOOH formation are less than 1% for this channel. Plots showing the rate constants’ unimolecular product channels for the decomposition of PAL2QJ and MH1QJ are similar and are shown in Figure 11D,F. For MPO1QJ, PAL1QJ, and PA1QJ, the barriers for intramolecular H transfer to form QOOH radicals are lower than those for the loss of O2 to give R•. The plot in Figure 11A shows the rate constants for the unimolecular decomposition of MPO1QJ, while the plots for PAL1QJ and PH1QJ are shown in Figure 11C,E. These rate

Figure 9. Comparison of pressure dependence of the reaction constants at 800 K for the products from R• + O2 for 2-pentyl radical (top) and hydroxypentyl radical from 1-pentanol (bottom).

For all of the radicals other than hydroxypentyl radical, pressure dependence similar to that shown for 2-pentyl radical was observed. Thus, in the ensuing analysis and discussion, we consider rate constants and branching ratios at 10 atm. At this pressure, the rate of reaction of R• + O2 to form ROO• is essentially the same for all radicals except for hydroxypentyl radical, POH1QJ. Differences in autoignition will be determined by the reaction of the ROO• radical and the subsequent QOOH species. For PN2QJ decomposition, the rate constants shown in Figure 10 are dominated by the formation of the 2hydroperoxypent-4-yl (PN2Q4J), QOOH (C4), radical at autoignition temperatures of 550−800 K. At these temperI


Article


hydrogen atom abstraction from pentanal. Alkyl groups adjacent to carbonyl groups have a low C−H BDE because of resonance stabilization of the resulting radical. However, this also leads to a low energy barrier for dissociation of the peroxy radical, ROO•, which competes with formation of QOOH, an important reaction in chain branching. Thus, the CN for these molecules is typically low. Alcohols have low CN because reaction of the peroxy radical to give aldehydes or ketones is fast and reduces the formation of QOOH. The fundamental insight elucidated by this work constitutes substantial progress toward a deeper understanding of the energetics of critical reactions for autoignition. Such advancements will facilitate high-throughput in silico evaluation of potential biofuel candidates in various high-efficiency combustion scenarios.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b04000. Structure of pentane (Figure S1); HOMO and HOMO− 1 molecular orbitals for methylpentyl ether radical at C1 (Figure S2); HOMO and HOMO−3 for heptanone radical at C1 (Figure S3); reaction scheme for the reactions of POH1J, PAL1J, PAL2J, HON1J, MPO1J, MH1J, and PA1J (Figures S4−S10); reactions of QOOH showing schematics of transition states (Figure S11); naming convention using pentanol as an example (Table S1); bond lengths of Cα−O bonds and Cβ−C(O) bonds of R• radicals (Table S2); and energy barriers of the chemical activation process in pentane (Table S3) (PDF)

Figure 11. Calculated rate constants for product formation from the reaction of ROO• peroxy radical in (A) pentylmethyl ether (MPO1QJ), (B) 2-heptanone (HON1QJ), (C) pantanal (PAL1QJ), (D) pantanal (PAL2QJ), (E) pentyl acetate (PA1QJ), and (F) methyl hexanoate (MH1QJ).

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AUTHOR INFORMATION

Corresponding Author

constants for the formation the QOOH radical are higher for PAL1QJ and MPO1QJ than that for PN2QJ, while for PM1QJ, the rate constants are approximately the same. Collectively, these results suggest that propanal and methylpentyl ethers should more readily form the QOOH radicals necessary for autoignition than pentane or pentyl acetate, confirming the high CN for these two molecules. For all of the molecules studied, reactions that compete with autoignition reactions increase in relative importance with increasing temperature. For instance, in Figures 10 and 11, as the temperature increases, the redissociation reactions of peroxy radicals to give R• + O2 and the reaction to produce an olefin + HO2 increase relative to the reactions to give QOOH. This suggests that autoignition will decrease with increasing temperature, confirming the negative temperature dependence often observed.

*E-mail: [email protected]. ORCID

Peter N. Ciesielski: 0000-0003-3360-9210 Seonah Kim: 0000-0001-9846-7140 Robert L. McCormick: 0000-0003-1462-7165 Thomas D. Foust: 0000-0002-3995-8254 Mark R. Nimlos: 0000-0001-7117-775X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to acknowledge constructive conversations with Han-Heinrich Carstensen (Ghent University). This research was conducted as part of the Co-Optimization of Fuels & Engines (Co-Optima) project sponsored by the U.S. Department of Energy (DOE) Office of Energy Efficiency and Renewable Energy, Bioenergy Technologies and Vehicle Technologies Offices. Co-Optima is a collaborative project of several national laboratories initiated to simultaneously accelerate the introduction of affordable, scalable, and sustainable biofuels and high-efficiency, low-emission vehicle engines. Work at the National Renewable Energy Laboratory was performed under Contract No. DE347AC36-99GO10337. Computer time was provided by the NSF Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF Grant No. ACI-1053575 and by the

4. CONCLUSIONS In this study, we have conducted a systematic comparison of autoignition chemical pathways of oxygen functional groups attached to five carbon molecules. Though this study only considered the addition of the first molecular oxygen, a forthcoming study has investigated the addition of a second molecular oxygen and additional reactions for radical chain branching. The quantum mechanical results in this work show that aldehydes and ethers have high CNs because of low barriers to form hydroperoxy radicals, QOOH, from peroxy radicals, ROO•, and because of favorable energetics for J


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National Renewable Energy Laboratory Computational Sciences Center.

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