Quantum Chemical Study of Cetane Improvers - American Chemical

having the cetane number increase effect and the relationship between the chemical ... various cetane improvers and compounds having no cetane number ...
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Energy & Fuels 2003, 17, 725-730

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Quantum Chemical Study of Cetane Improvers Takahiro Yonei, Kohtaro Hashimoto,* Mitsuru Arai, and Masamitsu Tamura Institute of Environmental Studies, Graduate School of Frontier Sciences, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan Received November 5, 2002

Quantum chemical calculations were performed in order to clarify the chemical properties for having the cetane number increase effect and the relationship between the chemical structure of the cetane improvers and their effects. The density functional theory (DFT) calculation, including the B3LYP calculation coupled to a 6-31+G(d) basis set, was used to estimate the thermochemical properties of the chemical compounds. First, the bond-dissociation energy of various cetane improvers and compounds having no cetane number increase effects were calculated to estimate the threshold value of the bond-dissociation energy necessary to have the cetane number increase effect. The result suggests that the 190-210 kJ/mol of the bonddissociation energy could be the threshold value of the bond-dissociation energy necessary to have the cetane number increase effect. Next, the reaction Gibbs free energies by oxygen addition reactions (-∆G) of various alkyl radicals that were produced from the thermal decomposition of the cetane improvers were calculated. The relationship between the reaction Gibbs free energy for the O2 addition reaction and cetane number increase by cetane improvers from which these alkyl radicals were produced were investigated. As a result, there is a positive correlation between -∆G and the cetane number improvement when comparing the radicals with the same molecular skeletons.

Introduction Diesel fuels having poor ignition properties would induce such problems as diesel knock and enginestarting difficulties in cold weather. Such diesel fuels need to have improved ignition properties. The ignition properties of diesel fuels can be rated in terms of their cetane number. Cetane number is defined by reference to the ignition properties of standard mixtures of hexadecane (cetane, cetane number 100) and 2,2,4,4,6,8,8heptamethylnonane (heptamethylnonane, cetane number 15) under standard test conditions. The cetane number of a test fuel is determined by using a CFR engine prescribed by the American Society for Testing and Materials (ASTM D613-84). The engine is operated under the conditions shown in Table 1. Reference fuels (the mixture of cetane and heptamethylnonane) having different cetane numbers within 5 cetane number intervals are used so that the cetane number of the test fuel can be determined by interpolation of the compression ratios of the two reference fuels. The addition of cetane improvers to diesel fuels is one method to improve the ignition properties of diesel fuels. In the 1940s and 1950s, organic peroxides were found to be effective cetane improvers as well as alkyl nitrates and other compounds.1 Li et al. examined the improvement in cetane number by some nitrates and organic peroxides and suggested that the improvement in the cetane number correlated with the number of free * Corresponding Author. Tel: +81-3-5841-7293. Fax: +81-3-58417224. E-mail: [email protected]. (1) Robbins, W. E.; Audette, R. R.; Reynolds, N. E. Soc. Automot. Eng. Q. Trans. 1951, 5, 404-417.

Table 1. Operation Conditions of the CFR Engine engine speed [rpm] intake air temperature [°C] injection timing [° BTDC] injection rate [mL/min]

900 ( 9 66 ( 0.5 13 13 ( 0.2

radicals produced by the thermal decomposition of the additive during the preignition period.2 Inomata et al. studied the effects of isopropyl nitrate and di-tert-butyl peroxide on the spontaneous ignition of n-butane using a rapid compression machine and concluded that the most important factor is the heat released by the combustion of the additive during the preignition period.3 Al-Rubaie et al. examined the effectiveness of some organic peroxides and nitrates in reducing the ignition delay period and concluded that the primary role of the additives was that of heat generation through rapid, exothermic, oxidative degradation following injection into the cylinder.4 Clothier et al. made engine measurements with several additives at a lower temperature than in a normally operating diesel engine.5 Clothier et al. also reviewed how the cetane improver worked.6 Oxley et al. investigated the thermal stabilities of the cetane improvers.7 Oxley et al. also investigated (2) Li, T.; Simmons, R. F. Twenty-First Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, 1986; pp 455462. (3) Inomata, T.; Griffiths, J. F.; Pappin, A. J. Twenty-Third Symposium (International) on Combustion; The Combustion Institute: Pittsburgh, 1990; pp 1759-1766. (4) Al-Rubaie, M. A. R.; Griffiths, J. F.; Sheppard, C. G. W. Soc. Aautomot. Eng. Pap. 1991, 91233. (5) Clothier, P. Q. E.; Moise, A.; Pritchard, H. O. Combust. Flame 1990, 82, 242-250. (6) Clothier, P. Q. E.; Aguda, B. D.; Moise, A.; Pritchard, H. O. Chem. Soc. Rev. 1993, 22, 101-108.

10.1021/ef020266m CCC: $25.00 © 2003 American Chemical Society Published on Web 04/15/2003

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the heat-release behavior of the cetane improvers using differential scanning calorimetry.8 Our study suggests that free radicals in the preignition period should play an important role in improving their ignition properties9 and that azo compounds, which are known to be radical-generating agents, improve the cetane number.10 Also, our study suggests that 2,2-dinitropropane would improve the cetane number by producing the 2-nitro-2-propyl radical.11 We have attempted to calculate the pressure-temperature profile for the spontaneous ignition of n-butane in the presence of cetane improvers.12 Furthermore, diesel fuels have been autoxidized in the liquid phase under various conditions and the cetane numbers of the autoxidized fuels have been investigated.13 As a result, it was shown that the cetane numbers of autoxidized fuels increased. We have also applied the cetane improvers to LPG (Liquefied Petroleum Gas) in order to utilize the LPG as a diesel fuel.14-18 Furthermore, we have investigated the effects of the cetane improvers on diesel exhaust emissions.19 It is necessary for the development of effective cetane improvers to clarify the chemical properties producing the cetane number increase effect. Also, it is important to elucidate the relationship between the chemical structure of the cetane improvers and their effects. On the other hand, quantum chemical calculations have become an effective tool due to the recent improvement in computer performance. If the clarification of the chemical properties producing the cetane number increase effect and the elucidation of the relationship between chemical structure of cetane improvers and their effects are possible using the quantum chemical calculation, the quantum chemical calculations can aid in the development of high-performance cetane improvers. In this study, quantum chemical calculations were performed in order to determine the chemical properties producing the cetane number increase effect and the relationship between the chemical structure of the cetane improvers and their effects. First, bond-dissociation energy of various cetane improvers and compounds having no cetane number increase effects were calculated in order to estimate the threshold value of the (7) Oxley, J. C.; Smith, J. L.; Rogers, E.; Ye, W.; Aradi, A. A.; Henly, T. J. Energy Fuels 2000, 14, 1252-1264. (8) Oxley, J. C.; Smith, J. L.; Rogers, E.; Ye, W.; Aradi, A. A.; Henly, T. J. Energy Fuels 2001, 15, 1194-1199. (9) Hashimoto, K.; Kawakatsu, Y.; Arai, M.; Tamura, M. J. Jpn. Inst. Energy 1995, 74, 200-204 (in Japanese). (10) Hashimoto, K.; Akutsu, Y.; Arai, M.; Tamura, M. Sekiyu Gakkaishi 1996, 39, 166-169 (in Japanese). (11) Hashimoto, K.; Yamada, H.; Ohno, Y.; Arai, M.; Tamura, M. Sekiyu Gakkaishi 1997, 40, 524-528 (in Japanese). (12) Hashimoto, K.; Akutsu, Y.; Arai, M.; Tamura, M. Sekiyu Gakkaishi 1998, 41, 341-347. (13) Hashimoto, K.; Ikeda, M.; Arai, M.; Tamura, M. Energy Fuels 1996, 10, 1147-1149. (14) Goto, S.; Lee, D.; Wakao, Y.; Honma, H.; Mori, M.; Akasaka, Y.; Hashimoto, K.; Motohashi, M.; Konno, M. Soc. Automot. Eng. Pap. 1999, 1999-01-3602. (15) Hashimoto, K.; Hirasawa, T.; Arai, M.; Tamura, M. Sekiyu Gakkaishi 2000, 43, 386-391. (16) Ohta, H.; Hashimoto, K.; Arai, M.; Tamura, M. Sekiyu Gakkaishi 2001, 44, 411-412. (17) Hashimoto, K.; Ohta, H.; Hirasawa, T.; Arai, M.; Tamura, M. Soc. Automot. Eng. Pap. 2002, 2002-01-0870. (18) Ohta, H.; Hashimoto, K.; Arai, M.; Tamura, M. J. Jpn. Pet. Inst. 2002, 45, 327-328. (19) Ohtsuka, A.; Hashimoto, K.; Akutsu, Y.; Arai, M.; Tamura, M. J. Jpn. Pet. Inst. 2002, 45, 24-31(in Japanese).

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Figure 1. Reaction mechanism of cetane number improvers.

bond-dissociation energy necessary to have the cetane number increase effect. Next, the reaction Gibbs free energies of the oxygen addition reactions (-∆G) of various alkyl radicals that were produced from the thermal decomposition of the cetane improvers were calculated. The relationship between the reaction Gibbs free energy of the O2 addition reaction and the cetane number increase by the cetane improvers from which these alkyl radicals were produced was investigated. Calculations Calculation Methods. The density functional theory (DFT) calculation, including the B3LYP calculation coupled to a 6-31+G(d) basis set, was used to estimate the thermochemical properties of the chemical compounds in this study. As the DFT calculation includes the effect of the electron correlation and can be calculated with a high accuracy, it needs only as much calculation time as the Hartree-Fock calculation, which is the cheapest ab initio calculation. The DFT calculations were performed using Gaussian 98.20 Reaction Mechanism for Cetane Improvers. Figure 1 shows the reaction of some cetane improvers. A cetane improver is decomposed to produce alkoxy radicals. The alkoxy radical produces an alkyl radical through β-fission. The addition reaction of an oxygen molecule to an alkyl radical produces an alkyl peroxy radical to enhance the preignition reaction of the diesel fuel.9 Our study has focused on the decomposition of the cetane improvers and the oxygen addition reaction of the alkyl radicals. It is necessary for a chemical compound to have a small bond-dissociation energy to be rapidly decomposed to produce a radical during the preignition reaction of the diesel engine in order to produce the cetane number increase effect. Therefore, it is important for the molecular design of the cetane improver to know the threshold value of the bond-dissociation energy necessary to produce the cetane number increase effect. The oxygen addition reaction of the alkyl radical is central to the nature of the oxidation process of hydro(20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.7; Gaussian, Inc., Pittsburgh, PA, 1998.

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Figure 3. Decomposition mechanism of azo compounds.

Figure 2. Skeletons and substituents of alkyl radicals.

carbons.21 As the oxygen addition reaction of the alkyl radical is an equilibrium reaction, this equilibrium of the alkyl radicals produced from the cetane improvers is one of the important factors to determine the cetane number improvement. Species for Calculation. Species for Bond Dissociation Energy Calculation. The bond dissociation energies of isoamyl nitrate, n-propyl nitrite, n-butyl nitrite, tertbutyl nitrite, n-amyl nitrite, isoamyl nitrite, di-tert-butyl peroxide, 2,2-dinitropropane, diethyl ether, nitromethane, nitroethane, and nitropropane were calculated. Isoamyl nitrate, isoamyl nitrite, n-propyl nitrite, n-butyl nitrite, n-amyl nitrite, tert-butyl nitrite, di-tert-butyl peroxide, and 2,2-dinitropropane provide the cetane number increase effect. On the other hand, diethyl ether, nitromethane, nitroethane, and nitropropane have little or no effect on the cetane number. Species for the Calculation of the Relationship between the Molecular Structure and Cetane Number Improvement. Alkyl radicals having the same molecular skeleton and different substituents have different cetane number increase effects. Therefore, the reaction Gibbs free energies of the oxygen addition reactions (-∆G) of three sets of molecular skeletons, the 2-substituted-2-butyl radical, 2-substituted-4-methyl-2-pentyl radical, and 1-substituted-cyclohexyl radical, were calculated. The substituents were a cyano group (-CN), methoxyl group (-OCH3), acetoxyl group (-OCOCH3), and propionoxyl group (-OCOC2H5). Figure 2 shows the structures and substituents. In addition to the reaction Gibbs free energies of the oxygen addition reactions, the ceiling temperatures of these alkyl radicals were calculated. The ceiling temperature is the temperature at which the concentration of the alkyl radical and alkyl peroxy radical become equal in the O2 addition reaction. The equilibrium constant of the O2 addition reaction is expressed as follows:

K)

[RO2] [R][O2]

)

PRO2/P° PR/P°‚PO2/P°

)

P° (P ) PR)‚‚‚ PO2 RO2

(1)

∴ K × PO2 ) P° () 1[atm]) And according to the relation of the equilibrium and Gibbs free energy,

-∆G ) RT ln K ‚‚‚

(2)

The ceiling temperature of each alkyl radical was calculated from eqs 1 and 2. The reaction Gibbs free energies of the oxygen addition reactions and the ceiling temperatures of the alkyl radicals were compared with the cetane number increase of the azo compounds which produce these alkyl radicals. The azo compounds were decomposed to produce alkyl radicals, as shown in Figure 3. Our previous study indicated that azo compounds also produced a cetane number increase, and that azo compounds having the same molecular skeleton and different substituents had different cetane number increases.10 In the study, kerosene (cetane number 45) was used as a base fuel. Estimation of the Threshold Value of the BondDissociation Energy. A more precise threshold value of the bond-dissociation energy necessary to have the effect of cetane number improvement was estimated by considering the frequency factor because the thermal decomposition rate of a species depends on not only the activation energy but also the frequency factor. Cetane improvers should be decomposed in a much shorter time period than the ignition delay period of the diesel fuel in the combustion chamber. Thus the half-lives of the compounds with various activation energies and the frequency factor values were calculated using the temperature of the CFR engine. The combustion chamber temperature was estimated by assuming an adiabatic compression. The compression ratio of the reference fuel having the cetane number of 40 was used for the estimation. As the ignition delay and engine speed of the CFR engine are fixed at 13 degrees of crank angle and 900 rpm, respectively, the ignition delay would be fixed at 2.41 ms. Thus, the half-life of the cetane improvers should be shorter than 2.41 ms. Results and Discussion Calculation of Bond-Dissociation Energy. Table 2 shows the calculated values of the bond-dissociation energies. A clear difference between the bond-dissociation energies of species having cetane number increase effects and those species not having cetane number increase effects is shown. Table 2 suggests that the threshold value of the bond-dissociation energy necessary to have the cetane number improvement effect would be between 170 and 250 kJ/mol. Table 2 also shows the bond-dissociation energies from the experiments. Although the calculated values of the bonddissociation energies of the di-tert-butyl peroxide and dinitropropane were smaller than their experimental values, a good correlation could be seen between the calculated values and experimental values of the other species. It is necessary for a chemical compound to have a low enough bond-dissociation energy to be rapidly decomposed to produce a radical during the preignition (21) Walker, R. W.; Morley, C. Low-Temperature Combustion and Autoignition; Pilling, M. J., Ed.; Elsevier Science B. V.: Amsterdam, The Nertherlands, 1997; pp 48-53.

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Table 2. Dissociation Energy of Species Used in Calculation calculated actual value value (kJ/mol) (kJ/mol)

species

Species having cetane number increase effects

n-propyl nitrite n-butyl nitrite n-amyl nitrite tert-butyl nitrite isoamyl nitrate isoamyl nitrite di-tert-butyl peroxide 2,2-dinitropropane

diethyl ether Species having no cetane nitromethane number increase effects nitroethane nitropropane a

Ref 22. b Ref 23. c Ref 24.

d

167.0 166.5 166.6 161.7 162.3 168.6 127.8 162.7

167.8a 177.8a

347.3 258.0 253.9 254.6

352.2c,d 251.0e 251.2d,e,f 258.2d,e,f

172.0a 159.0a 191.2b

Ref 25. e Ref 26. f Ref 27.

Table 3. Compression Ratio, Calculated Temperature in the Combustion Chamber of the CFR Engine compression ratio

temperature [°C]

13.2

677

Table 4. Calculated Half-lives (ms) with Various Values of E (kJ/mol) and A (1/s) E (kJ/mol)

A ) 1013 (1/s)

A ) 1014 (1/s)

A ) 1015 (1/s)

A ) 1016 (1/s)

180 190 200 210 220 230 240 250 260

5.88 × 10-1 2.09 7.46 2.66 × 10 9.46 × 10 3.37 × 102 1.20 × 103 4.27 × 103 1.52 × 104

5.88 × 10-2 2.09 × 10-1 7.46 × 10-1 2.66 9.46 3.37 × 10 1.20 × 102 4.27 × 102 1.52 × 103

5.88 × 10-3 2.09 × 10-2 7.46 × 10-2 2.66 × 10-1 9.46 × 10-1 3.37 1.20 × 10 4.27 × 10 1.52 × 102

5.88 × 10-4 2.09 × 10-3 7.46 × 10-3 2.66 × 10-2 9.46 × 10-2 3.37 × 10-1 1.20 4.27 1.52 × 10

reaction of the diesel engine in order to provide a cetane number improvement. Generally, the activation energy of the dissociation reaction is comparable to the bonddissociation energy. According to the Arrhenius equation, the activation energy exponentially affects the rate of the dissociation reaction. The estimated combustion chamber temperature of a CFR engine is shown in Table 3. As the ignition delay of the CFR engine is fixed at 2.41 ms, the half-life of the cetane improvers should be shorter than 2.41 ms. Table 4 shows the calculation result of the half-lives of the compounds with various activation energies and the frequency factor values. The meshed columns of Table 4 show the half-lives, which are shorter than 2.41 ms. The frequency factor of a unimolecular decomposition is usually in the range between 1013 and 1015. The 190210 kJ/mol of the bond-dissociation energy could be the threshfold value of the bond-dissociation energy necessary to produce the cetane number increase effect. As the frequency factor and the activation energy of the 2,2-dinitropropane dissociation reaction are about 1013.1/s and 191.2 kJ/mol, respectively, its half-life at 950 (22) Batt, L.; McCulloch, R. D.; Milne, R. T. Int. J. Chem. Kinet. 1975, 441-461. (23) Zhang, Y. X.; Bauer, S. H. J. Phys. Chem. A 2000, 104, 12171225. (24) Pihlaja, K.; Heikkil, J. Acta Chem. Scand. 1968, 22, 2731-2732. (25) Tsang, W. Blackie Academic and Professional: London, 1996; pp 22-58. (26) Dewar, M. J. S.; Ritchie, J. P.; Alster, J. J. Org. Chem. 1985, 50, 1031-1036. (27) Chen, P. C.; Wu, J. C.; Chen, S. C. Comput. Chem. 2001, 25, 439-445.

Figure 4. Relationship between the reaction Gibbs free energy of the O2 addition reaction (-∆G) and cetane number increase (∆CN). Table 5. Calculated Values of the Reaction Gibbs Free Energy (kJ/mol) of the O2 Addition Raction 2-substituted1-substituted1-substituted4-methylsubstituent 1-butyl radical cyclohexyl radical 2-pentyl radical -CN -OCOCH3 -OCH3 -OCOC2H5

-4.0 -62.8

-7.6 -73.5 -84.2 -64.9

7.7 -49.6 -57.9 -51.9

K was calculated to be 1.8 ms, which was shorter than 2.41 ms. Also, the bond-dissociation energies of the species having no cetane number increase effects were greater than 210 kJ/mol. These data suggest that the 190-210 kJ/mol bond-dissociation energy is the threshold value to produce the cetane number increase effect. Relation between Molecular Structure and Cetane Number Improvement. Table 5 shows the calculated values of the reaction Gibbs free energy of the O2 addition reaction (-∆G). Table 4 indicates that the cyano group (-CN), has the smallest -∆G values and the methoxyl group (-OCH3) has the largest value. Table 5 suggests that radicals with methoxyl group would be able to undergo the oxygen addition reaction. Figure 4 shows the relationship between the reaction Gibbs free energy of the O2 addition reaction of the alkyl radicals and cetane number increase of kerosene by 0.01 mol/L of azo compounds from which these alkyl radicals were produced. This figure shows that there is a positive correlation between -∆G and the cetane number improvement for the radicals with the same molecular skeletons. Alkyl radicals having larger -∆G values would generate more alkyl peroxy radicals that underwent further reactions in Figure 1 to enhance the preignition reaction. Table 6 shows the calculated values of the ceiling temperature. Table 6 indicated that the cyano group (-CN) has the lowest ceiling temperature and the methoxyl group (-OCH3) has the highest one. Figure 5 shows the relation between the ceiling temperature of

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Energy & Fuels, Vol. 17, No. 3, 2003 729

Figure 6. Relationship between -∆G and atomic spin density. Table 7. -∆G Value and Atomic Spin Density of 4-Methyl-Pentyl Radical with Various Substituents

Figure 5. Relationship between the ceiling temperature (K) and cetane number increase (∆CN). Table 6. Calculated Values of Ceiling Temperature (K) of Alkyl Radicals 2-substituted1-substituted1-substituted4-methylsubstituent 1-butyl radical cyclohexyl radical 2-pentyl radical -CN -OCOCH3 -OCH3 -OCOC2H5

350 700

380 810 900 710

280 620 700 640

the alkyl radicals and cetane number increase of kerosene by 0.01 mol/L of azo compounds from which these alkyl radicals were produced. Figure 5 shows that the increase in the ceiling temperature of the alkyl radical produces a hyperbolical increase effect on the cetane number. As the ceiling temperature is higher than the temperature of the combustion chamber, the concentration of the alkyl peroxy radicals would be drastically increased. Thus, it is important for the effective cetane improver to produce the alkyl radical whose ceiling temperature is higher than that of the combustion chamber. The substituent effects of the alkyl radicals can be qualitatively explained by the classical electroorganic theory. As the cyano group, that is a typical electronwithdrawing group, delocalizes the unpaired electron of the alkyl radial, this group lowers the reaction Gibbs free energy of the O2 addition reaction of the alkyl radical because the delocalized unpaired electron is less reactive. Similarly, as the methoxyl group is a typical electron-releasing substituent, the unpaired electron of the alkyl radical was localized to raise the reaction Gibbs free energy of the O2 addition reaction. These ideas can explain the high cetane number increase effect of n-butoxyethyl nitrate.2 Thermal decomposition of n-butoxyethyl nitrate produces the n-butoxymethyl radical. The unpaired electron of the n-butoxymethyl radical seems to be localized by the n-butoxy group to enhance the reaction Gibbs free energy of the O2 addition reaction.

substituent

-∆G (kJ/mol)

atomic spin density

-CN -OCOCH3 -OCOC2H5 -OCH3 -OH -NO2 -NH2 -CHO -NHCH3 -OC2H5 -COOH

-7.70 49.59 51.88 57.94 76.71 10.07 68.75 2.20 29.83 72.47 6.72

0.8304 0.9298 0.9497 1.0766 1.0010 0.7709 0.9821 0.7533 0.9795 0.9497 0.8467

Since a radical has an odd number of electrons, its frontier orbital is called Singly Occupied Molecular Orbital (SOMO) where one R-spin electron (unpaired electron) is located. Thus it is very important to consider how an R- spin electron is localized. The localization of an R-spin electron is expressed in terms of the atomic spin density of a carbon atom having unpaired electron. Therefore, -∆G and an atomic spin density of that carbon atom of the 4-methyl-2-pentyl radical with various substituents were calculated. Table 7 shows the calculation values of -∆G and atomic spin density. Table 7 shows that radicals with an electron-withdrawing substituent have a small -∆G value and atomic spin density value. Figure 6 shows the relationship between the -∆G and the atomic spin density. Figure 6 indicates the positive correlation between -∆G value and the atomic spin density. Thus, alkyl radicals having electronreleasing substituents are expected to have a higher cetane number increase effect because they have higher Gibbs free energy of the O2 addition reaction due to the localization of R-spin electrons. The cetane number increase effects by alkyl radicals are dependent not only on the addition reactivity of oxygen but also on the molecular skeletons. Among the three sets of molecular skeletons, the cetane number increase by 2-substituted-4-methyl-2-pentyl radicals was the highest with the same substituents. Our previous study suggested that alkyl radicals having a longer carbon chain produced a higher cetane number increase.9 For development of effective cetane improvers, it is necessary to search for compounds which produce

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alkyl radicals having a longer carbon chain and a higher reaction Gibbs free energy of the O2 addition reaction. Conclusion Density functional theory calculations were performed in order to clarify the chemical properties producing the cetane number increase effect and the relationship between the chemical structure of cetane improvers and their effects. First, the bond-dissociation energy of various cetane improvers and compounds having no cetane number increase effects were calculated in order to estimate the threshold value of the bond-dissociation energy necessary to produce the cetane number increase effect. The results suggest that the 190-210 kJ/mol of bond-dissociation energy could be the threshold value of the bond-dissociation energy necessary to have the

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cetane number increase effect. Next, the reaction Gibbs free energies of the oxygen addition reactions (-∆G) of various alkyl radicals that were produced from the thermal decomposition of the cetane improvers were calculated. The relationship between the reaction Gibbs free energy of the O2 addition reaction and the cetane number increase by the cetane improvers from which these alkyl radicals were produced were then investigated. As a result, there is a positive correlation between -∆G and the cetane number improvement for the radicals with the same molecular skeletons. Acknowledgment. The authors thank Prof. Mitsuo Koshi, The University of Tokyo, Graduate School of Engineering, for acting as an advisor for this research. EF020266M