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Structures and Energetics of Unimolecular Thermal Degradation of Isopropyl Butanoate as a Model Biofuel: Density Functional Theory and Ab Initio Studies Ahmed M. El-Nahas,* Lobna A. Heikal, Ahmed H. Mangood, and El-Sayed E. El-Shereefy Chemistry Department, Faculty of Science, El-Menoufia UniVersity, Shebin El-Kom, Egypt ReceiVed: April 15, 2010; ReVised Manuscript ReceiVed: June 21, 2010
Density functional theory (DFT)/BMK and CBS-QB3 ab initio calculations have been carried out to study the structures and energetics of unimolecular decomposition reactions of isopropyl butanoate (IPB, C3H7C(O)OCH(CH3)2) as a model biofuel. The results show a good performance of the BMK method. Among seven different dissociation channels of IPB, formation of butanoic acid and propene via a six-membered ring transition state is the most favorable reaction. On the other hand, formation of lower esters is hindered by high-energy barriers and unlikely occurs except at elevated temperatures. Simple bond scission costs less energy than lower ester formation. A comparison with methyl and ethyl esters indicates faster decomposition of IPB. The changes in bond lengths along minimum energy paths are discussed. 1. Introduction Increased demand for energy, climate change, air pollution, the higher cost for crude oil, and limited reserves of fossil fuel together push the search for alternative renewable fuels. Biofuels represent very promising sources of energy for the transportation sector, which will lessen the dependence on petroleum. They produce fewer greenhouse gases than fossil fuels and have the potential to reduce soot emissions.1 Biofuel can be produced from different biomasses. One important class of biofuels consists of large methyl and ethyl esters derived from vegetable and animal oils and fats.2-6 This is the biodiesel which is a renewable fuel that is expected to relieve demand for imported fossil fuel. Biodiesel is suitable for use within the current transport sector infrastructure, as it has physical properties similar to those of conventional diesel fuel.7 Some experimental and few theoretical studies have been reported for real biofuel.8-24 Direct studies of typical biodiesels are difficult because experiments would have to be carried out on complex, largely involatile mixtures and also because of the computational cost needed for such large molecules. However, better understanding of the combustion mechanism can be accomplished using a model biofuel. For practical reasons it is more convenient to use simple molecules for combustion modeling. Experimental25-44 and theoretical43-47 work has been done on model esters. These small esters include the ester moiety and part of the carbon chain in the acid side and, therefore, can be used to provide insights into the combustion chemistry of the real biodiesel. One of the problems of biodiesel is its performance in cold weather. The crystallization properties of methyl and ethyl biodiesel esters can be improved by introduction of branching.48,49 Methyl and ethyl esters of fatty acid have been intensively studied. Introduction of branching into a linear, long-chain ester is expected to disrupt intermolecular associations at low temperatures, which reduces the crystallization temperature. The crystallization point of isopropyl soyate (IPS) was found be lower than that of methyl soyate (MS) (-9 vs -2 °C, respectively).50 IPS has emission behavior similar to that of MS * To whom correspondence should be addressed. E-mail: amelnahas@ hotmail.com.
and superior low-temperature performance.50 Moreover, the cetane numbers of fatty acid esters are not altered significantly by branching in the alcohol moiety.19 Branching decreases the viscosity of fatty acid esters.51 Therefore, studying isopropyl ester as a model biodiesel will shed some light onto the combustion behavior of a branched ester as a biodiesel. There are some experimental studies on isopropyl acetate and isopropyl propanoate esters concerned with determination of the rate coefficients of their unimolecular decompositions.52-61 Only one theoretical study has been reported on the mechanistic details of pyrolysis of isopropyl acetate to propene and acetic acid.62 Better simulation of fatty acid esters can be achieved by increasing the alkyl chain length at the acid side. Therefore, we expect esters of butanoic acid to be better than either acetic or propanoic acid analogues. The six-centered decomposition channel is the dominant reaction for alkyl esters.25,29,30,45 Branching at the alcohol side of the ester increases the rate of decomposition compared to that of methyl, ethyl, and propyl esters.34 Branching has been shown to reduce the activation energy for ester six-centered decomposition reactions by 12.5-23 kJ/mol.63 Isopropyl butanoate (IPB) has some advantages as a biofuel. Its carbon content fits with the number of carbons in gasoline, and therefore, it can be considered as a real biogasoline (high flash point compared to that of biobutanol). With increasing branching, the octane number is expected to increase. IPB is highly flammable and not corrosive compared to bioethanol. It does not need any additives as its freezing point is high. Therefore, it does not freeze in winter. To the best of our knowledge, there are a few experimental studies and no theoretical studies on IPB regarding its unimolecular decomposition. Most of the studies on IPB concentrated on one dissociation reaction, namely, the production of butanoic acid and propene. An earlier study declared that the enol form of the corresponding acetate ester (alkoxyvinyl alcohol, CH2dC(OH)OR) is one of the observed channels in the decomposition of esters having a γ-hydrogen.64 In this paper we describe the initial results from our ongoing work on thermochemistry and kinetics of pathways of decomposition of some branched esters. Low-temperature combustion usually dominates oxidative decomposition and thermal decom-
10.1021/jp103397f 2010 American Chemical Society Published on Web 07/12/2010
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position. Oxidative decomposition needs oxidizing agents to proceed. In this study we are interested in thermal degradation in the absence of air. Several dissociation channels of IPB as a model biofuel have been examined using density functional theory (DFT) and ab initio quantum chemical calculations. Compared to the most popular B3LYP method,65-67 BMK (Boese-Martin for kinetics)68 was developed for exploring potential energy surfaces and reaction mechanisms with an accuracy in energy barriers of 2 kcal/mol for the investigated benchmark calculations. The BMK method belongs to hybrid meta generalized gradient approximation (HM-GGA) functionals which include the spin density and its gradient, the spin kinetic energy density, and Hartree-Fock (HF) exchange.68 The amount of Hartree-Fock (HF) exchange in BMK is 42% compared to 20% in B3LYP.65-68 It is worth judging the BMK performance against high-level ab initio calculations and/or experiment, if any. The structures and energetics of IPB, the products, and the corresponding transition states are discussed. A comparison with other esters is taken into account. This paper is organized as follows: Section 2 gives the details of the computational methods. Section 3 presents the results and discussion and is divided into three subsections for analyzing decomposition reactions of IPB. This is followed by section 4, which summarizes the main conclusions derived from the current study. 2. Computational Details Electronic structure calculations were performed using the Gaussian 03 program.69 Geometry optimizations without symmetry constraints have been carried out for IPB, the transition states, and the products at the DFT/BMK/6-31+G(d,p) level (hereafter called L1). The search for the transition states for unimolecular dissociation of the investigated ester has been carried out using the eigenvalue-following (EF) optimization procedures as implemented in the Gaussian program. For each stationary point, vibrational frequency calculations have been conducted at the same level used for optimization to characterize its nature as a minimum (positive frequencies) or transition state (only one negative frequency) and to correct the energies for zero-point and thermal contributions at 298 K. The vibrational modes were examined using the ChemCraft application70 to verify the existence of the transition states. To further ensure that the located transition states connect the desired reactants and products, we determined the minimum energy path (MEP) connecting reactants to products through intrinsic reaction coordinate (IRC) calculations in mass-weighted Cartesian coordinates with a step size of 0.05 amu1/2 bohr.71,72 Energy refinement has been carried out at the BMK/6-311++G(2d,2p)// BMK/6-31+G(d,p) level (hereafter called L2) as well as at CBSQB3 multilevel computations for the seven dissociation channels. Unless noted otherwise, structures optimized using the L1 method and energies calculated at the L2 level will be considered. 3. Results and Discussion The optimized structures of IPB and the transition states for the butanoic acid and acetone formation reactions are displayed in Figure 1. Detailed structures and energetics of the transition states and products are given as Supporting Information. Bond dissociation energies (BDEs) for individual bonds are shown in Figure 2. A plot of L2 energy barriers against CBS-QB3 values for unimolecular decomposition reactions of IPB is shown in Figure 3a, while the corresponding plot for methyl butanoate (MB), ethyl propanoate (EP), and IPB at L1 vs CBS-QB3 is
Figure 1. Optimized structures of IPB, IPBTS1, and IPBTS2 at BMK/ 6-31+G(d,p).
displayed in Figure 3b. Variations of some bond distances along the reaction coordinates for the seven pathways are plotted in Figures 4-10. Potential energy profiles along the MEP of the isopropyl butanoate unimolecular decomposition reactions versus the reaction coordinate are displayed in Figure 11. Figure 12 depicts the potential energy diagram for all of the investigated reactions at the L1, L2, and CBS-QB3 levels of theory. The energies of the transition states and products are calculated relative to that of IPB. Unimolecular decomposition can proceed either through simple bond fission or via hydrogen transfer with bonds breaking and forming simultaneously. In this study we will concentrate on the latter case with brief referral to simple bond scission. IPB has many hydrogens that can migrate from different carbons to other atoms via four- or six-center transition states. These hydrogen transfers are referred to as 1,3- and 1,5-hydrgen shift reactions, respectively. Hydrogen migration within the butyl side of IPB gives rise to four reactions, namely, formation of lower esters (two channels), enol, and isopropyl vinyl alcohol (CH2dC(OH)OCH(CH3)2). Hydrogen transfer in the isopropyl side yields two channels, formation of butanoic acid and two carbonyl compounds. Hydrogen shift from the R carbon to the saturated oxygen atom produces ethyl ketene and isopropyl alcohol. These pathways can be summarized as follows:
C3H7C(O)OCH(CH3)2 f C3H7C(O)OH + CH3CHdCH2 (1)
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C3H7C(O)OCH(CH3)2 f C3H7C(O)H + CH3C(O)CH3 (2) C3H7C(O)OCH(CH3)2 f CH3CH2CHdC(OH)OCH(CH3)2 (3) C3H7C(O)OCH(CH3)2 f C2H5CHdCdO + (CH3)2CHOH (4) C3H7C(O)OCH(CH3)2 f CH2dC(OH)OCH(CH3)2 + CH2dCH2
(5)
C3H7C(O)OCH(CH3)2 f CH3C(O)OCH(CH3)2 + CH2dCH2
(6)
C3H7C(O)OCH(CH3)2 f HC(O)OCH(CH3)2 + CH3CHdCH2
(7)
With the exception of enolization, all channels are considered as β-scission reactions. The feasibility of the hydrogen transfer reaction will depend on the strength of the forming and breaking bonds as well as on factors that stabilize transition states such as ring size or some electronic effects. Two pathways occur through 1,5-hydrogen transfer reactions, formation of butanoic acid and isopropoxyvinyl alcohol, and occur through sixmembered ring transition states denoted by IPBTS1 and IPBTS5, respectively. The remaining five channels belong to 1,3hydrogen shift reactions. These include formation of acetone, ketene, enolization, and two lower esters via four-center transition sates: IPBTS2, IPBTS3, IPBTS4, IPBTS6, and IPBTS7, respectively. All of the investigated channels are endothermic, and according to the Hammond postulate,73 the structures of the transition states should be closer to those of the products rather than those of the reactants. However, it will depend on the endothermicity of the reaction. The calculated BDEs indicate that the CR-Cβ bond is the weakest bond followed by the CR-CO bond, Figure 2. The other C-C bonds in both sides of the ester group are of comparable BDEs (362-365 kJ/mol). The Cβ-H bond of the isopropyl group is the strongest bond in the whole molecule (BDE ) 435.7 kJ/mol). Conversely, the CR-H is the weakest C-H bond in MB, EP,45 and IPB (∼393 kJ/mol), and it clearly shows that this will be the hydrogen of choice for abstraction by oxidizing agents such as O2, O2H, or OH radicals. In the absence of hydrogen transfer unimolecular decomposition reactions, the CR-Cβ bond scission will be the dominant path in the pyrolysis of the three mentioned esters. An inspection of Figure 3 shows that the correlation between energy barriers calculated at BMK/6-31+G(d,p) or BMK/6-
Figure 2. Bond dissociation energies of IPB at BMK/6-311++G(2d,2p) (kJ/mol).
Figure 3. (a) Correlation between energy barriers (kJ/mol) for unimolecular decomposition channels of IPB. (b) Correlation between energy barriers (kJ/mol) for unimolecular decomposition channels of MB, EP, and IPB.
311++G(2d,2p)//BMK/6-31+G(d,p) and CBS-QB3 for the seven reactions is excellent and indicates that we can benefit from this by enlarging the ester and use BMK calculations with a reasonable degree of accuracy. The feasibility and difficulty in accessing some of the reactions can be well reproduced using the BMK method. Full details of the geometrical changes along the reaction path are given only for the least energy demanding processes, namely, the channels leading to butanoic acid and acetone. Other pathways will be discussed only briefly. 3.1. Formation of Butanoic Acid and Propene. The imaginary frequency reported for IPBTS1 is -1370 cm-1. Examination of this mode indicates a simultaneous stretching of the O1-H10 and C7-H10 bonds, which leads to the hydrogen migration reaction. The value of the imaginary frequency gives us information about the curvature of the potential energy surface (PES) at the TS along the imaginary mode. If the curvature is strong, we should have a large frequency as in the current case, while if the PES shows a low curvature, a lower frequency is obtained, sometimes below 100 cm-1.74 However, it depends on the level of theory. A higher curvature implies that the tunnel effect should be considered in reaction rate calculations especially at low temperatures. As shown in Figure 1, on going from IPB to IPBTS1, the C5-O2 bond is elongated by 0.611 Å and is virtually broken. Similarly, the C7-H10 bond distance is stretched by 0.218 Å (18.3%). The forming O1-H10 bond is stretched in IPBTS1 by 36.5% compared to that in butanoic acid. For bond angles, the major changes on going from IPB to IPBTS1 were recorded
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Figure 4. Variation of some bond distances along the reaction coordinate for butanoic acid formation.
for O2-C5-H8 (from 102° to 110°), H9-C7-H10 (109° vs 102.3°), and H10-C7-C5 (111° vs 97°). Figure 4 displays changes in some selected bond distances along the reaction path from IPB (right side) to the products (left side) passing through IPBTS1 (s ) 0.0 amu1/2 bohr). An inspection of Figure 4 indicates that the C5-O2 bond breaks before the C7-H10 bond and the latter lengthens gradually and looks broken at s ) -0.6 amu1/2 bohr. Earlier rapture of the C-O bond before the C-H bond can be attributed to the low BDE of the former bond, Figure 2. On the other hand, the O1-H10 bond length decreases with the progress of the reaction to reach its normal value in the products (butanoic acid) at s ) 0.6 amu1/2 bohr. Starting from IPB, double and single bond formation (C4-O2 and C4-O1, respectively) shows slight changes with the progress of the reaction. Kinetically and thermodynamically, this route represents the most feasible reaction among all channels with an energy barrier and reaction energy of 190 and 56 kJ/mol, respectively; see Figure 12. The weakest CR-Cβ bond needs 342 kJ/mol for homolytic bond cleavage, which is more energy demanding than the reaction leading to butanoic acid. The barrier height for the acid formation reaction calculated using the BMK method is lower than the CBS-QB3 value by 10-13 kJ/mol. Compared to experiment, the calculated activation energy for elimination of propanoic acid from EP is overestimated at CBS-QB3 by 9 kJ/mol.45 This might give evidence for the accuracy of barrier heights from BMK calculations. EP has been found to burn faster than MB due to the absence of the six-center intermediate in the latter.25,34,45,63 Comparing unimolecular degradation reactions of EP and IPB indicates that the latter decomposes faster in accord with previous findings of easier pyrolysis of branched esters.34,63 3.2. Acetone, Enol, and Ketene Formation Reactions. These reactions proceed through hydrogen migration from CR from both sides of the ester group to either oxygens or carbon atoms with formation of a CdC bond. For the acetone channel, the imaginary frequency in IPBTS2 is -949 cm-1. This mode corresponds to stretching of the C4-H8 and H8-C5 bonds involved in the hydrogen transfer reaction. Figure 1 shows that, on going from IPB to IPBTS2, the C4-O2 and C5-H8 bond distances are elongated by 0.434 and 0.377 Å, respectively. Compared to its value in butanaldehyde, the newly formed C4-H8 bond is increased in IPBTS2 by 0.168 Å. The C4-O1 and O2-C5 distances are slightly changed. Figure 5 displays the changes in active bonds during
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Figure 5. Variation of some bond distances along the reaction coordinate for acetone formation.
Figure 6. Variation of some bond distances along the reaction coordinate for enol formation.
the course of acetone formation. It is clear that the C4-O2 bond dissociates before any noticeable change in the C5-H8 bond. The latter started to stretch considerably only at s ) -1 amu1/2 bohr, passing through the zero reaction coordinates (IPBTS2) and then continuing in the direction of the products (acetone and butanaldehyde). On the other hand, the forming C4-H8 bond decreases with the progress of the reaction to form butanaldehyde. Acetone formation passes through an energy barrier of 280 kJ/mol. This is the second favorable channel both kinetically and thermodynamically with a reaction energy of 70 kJ/mol. This reaction costs less energy than homolytic breaking of the weakest CR-Cβ bond. The corresponding channel (formation of aldehydes) in the case of EP is the next energy demanding process after the acid formation process both thermodymanically and kinetically. On the other hand, elimination of aldehydes from MB competes with the enolization reaction.45 Reaction path profiles displayed in Figures 6 and 7 indicate that the most important geometrical changes are observed for O1,2-H2 and C1-H2 bonds and the breaking of the C4-O2 bond starts before that of the C1-H2 bond. Starting from IPB (right side), the C1-H2 bond is gently elongated until s ) 1 amu1/2 bohr, and then a remarkable stretch is observed passing through the IPBTS3 and IPBTS4 transition states. The bond looks like it is entirely broken beyond s ) -1 amu1/2 bohr. The O1,2-H2 bonds show the opposite behavior. The C4-O1 and C1-C4 distances are slightly changed during the course
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Figure 7. Variation of some bond distances along the reaction coordinate for ketene formation.
of transformation to the products. On the other hand, during ketene formation the breaking C4-O2 bond is considerably changed along the reaction path. Enol formation requires an activation energy of 307 kJ/mol and endothermicity of 127 kJ/mol. The enolization process demands an intermediate energy compared to other channels for IPB, MB, and EP.45 The importance of enol formation in both atmospheric and combustion chemistry for acids, esters, and aldehydes has been reported over the past four decades.66,75,76 There is one extra conjugation in enols compared to the parent molecules. Enols are stabililized because of resonance between the newly formed double bond and the enol hydroxyl group beside the carbonyl, hydroxyl, or alkoxy group of the parent aldehyde, acid, or ester, respectively.66,75,76 The decomposition of IPB to ketene passes through a barrier of 311 kJ/mol. Comparable barrier heights were found for the same channel in the case of EP and MB (314 and 311 kJ/mol, respectively), which can be ascribed to the close strengths of the CR-H bonds of ∼393 kJ/mol reported for the three esters. Thermodynamically, ketene formation is less favored than the enolization process by 20 kJ/mol. For MB and EP, the ketene formation channel is more endothermic than the enol reaction by 44 and 46 kJ/mol, respectively. The homolytic cleavage of the weakest CR-Cβ bond in IPB is still uncompetitive with either enolization or ketene formation. 3.3. Vinyl Alcohol and Lower Ester Formation. The hydrogen transfer from either Cβ or Cγ to CR, carbonyl carbon, or oxygen leads to formation of isopropyl acetate, isopropyl formate, or isopropoxyvinyl alcohol and ethene, respectively. Isopropoxyvinyl alcohol represents the enol form of the isopropyl acetate. Changes of active bond lengths along minimum energy paths of these reactions are depicted in Figures 8-10. The same features reported for the previous channels can also be observed on analyzing these figures. The energy barrier for the formation of isopropoxyvinyl alcohol is 300 kJ/mol. The low barrier reported in this case results from the stability of the six-center transition state. Elimination of methoxyvinyl alcohol from MB was found to be the fastest among other decomposition reactions due to the absence of a longer carbon chain in the alcohol side with labile β-hydrogens.45 The pyrolysis of EP cannot afford either ethoxyvinyl alcohol or ethyl acetate due to the lack of a γ-hydrogen.45,64 Reactions leading to isopropyl acetate and formate require 448.5 and 492.8 kJ/mol, respectively, to overcome the energy barriers. Elimination of formate from either EP or MB represents
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Figure 8. Variation of some bond distances along the reaction coordinate for vinyl alcohol formation.
Figure 9. Variation of some bond distances along the reaction coordinate, bohr amu1/2, for acetate formation.
Figure 10. Variation of some bond distances along the reaction coordinate for formate formation.
the least favored process. Compared to other channels on the PES of unimolecular decomposition of IPB, lower ester formation shows a moderate endothermicity. A reaction that produces isopropoxyvinyl alcohol is less favored compared to isopropyl acetate and formate pathways with reaction energies of 221, 95, and 127 kJ/mol, respectively. The BDEs reported for IPB are lower than the activation energies required to form lower esters, which indicates that the latter are unlikely produced
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J. Phys. Chem. A, Vol. 114, No. 30, 2010 8001 and formate channels, all of the investigated reactions cost less energy than simple bond scission. (3) Formation of propanoic and butanoic acids via six-membered ring transition states is the most favorable route both thermodynamically and kinetically in the thermal decomposition of IPB and EP, respectively. (4) IPB burns faster than either EP or MB. This reflects the influence of branching at the alcohol side of a given ester. (5) Enol formation represents important reaction pathways in the pyrolysis of IPB. (6) Further studies on branching, the chain length, and unsaturation at the acid side of esters are needed for fully understanding the mechanism of burning of different esters as biofuel.
Figure 11. Potential energy profile along MEP from the IRC calculation of IPB decomposition reactions.
Acknowledgment. We thank the Faculty of Science, ElMenoufia University, for use of the computational facility. We also thank Professor K. Hirao (RIKEN, Japan) and Professor T. Taketsugu (Hokkaido University, Japan) for giving us the opportunity to run a few calculations on their machines. Supporting Information Available: Optimized structures and energies of IPB, seven transition states, and the corresponding products. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes
Figure 12. Energy profile for unimolecular decomposition of IPB (∆E0, ∆E0q, kJ/mol) at BMK/6-31+G(d,p), BMK/6-311++G(2d,2p)//BMK/ 6-31+G(d,p) (bold italic), and CBS-QB3 (in parentheses).
except at elevated temperatures. Production of methyl and ethyl formates from MB and EP is also hindered by higher energy barriers.45 4. Conclusions In this work, unimolecular decomposition reactions of IPB were investigated. The calculations were carried out at the BMK/ 6-31+G(d,p), BMK/6-311++G(2d,2p), and CBS-QB3 levels of theory. Comparison with lower linear esters (EP and MB) has also been included. The results obtained can be summarized as follows: (1) Values of the energy barriers and bond dissociation energies for the three esters calculated at BMK correlate well with CBSQB3 values. This justifies studying of larger esters at BMK with reasonable accuracy. (2) With the exception of isopropyl acetate
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