Low-Temperature Oxidation Kinetics of Biodiesel Molecules: Rate

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A: Kinetics, Dynamics, Photochemistry, and Excited States

Low-Temperature Oxidation Kinetics of Biodiesel Molecules: Rate Rules for Concerted HO Elimination from Alkyl-Ester Peroxy Radicals 2

Xuan T. Le, Tam V.-T. Mai, Kuang C. Lin, and Lam K Huynh J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b05070 • Publication Date (Web): 10 Sep 2018 Downloaded from http://pubs.acs.org on September 10, 2018

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The Journal of Physical Chemistry

Low-Temperature Oxidation Kinetics of Biodiesel Molecules: Rate Rules for Concerted HO2 Elimination from Alkyl-Ester Peroxy Radicals Xuan T. Lea,b, Tam V.-T. Maia,b, Kuang C. Linc and Lam K. Huynhd*

a

Institute for Computational Science and Technology at Ho Chi Minh City, Vietnam University of Science, Vietnam National University-HCMC, Vietnam c Department of Mechanical and Electromechanical Engineering, National Sun Yat-Sen University, Kaohsiung, 80424, Taiwan d International University, Vietnam National University-HCMC, Vietnam b

------*

Corresponding author. Email address: [email protected] and [email protected] (LKH)

Tel: (84-8) 2211.4046 (Ext. 3233) Fax: (84-8) 3724.4271

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT In an attempt to construct detailed kinetic mechanisms for biodiesel fuels on the fly, highpressure rate rules for the concerted HO2 elimination reaction class were derived using a comprehensive training reaction set of more than 60 reactions involving different alkyl methyl/ethyl ester peroxy radicals (RCOOR’)-OO·. Using the composite electronic structure method CBS-QB3 in combination with classical statistical mechanics and the transition state theory (TST) rate model, high-pressure rate constants for the reactions in the training set as well as thermodynamic properties for the species involved were calculated. The corrections from Eckart tunneling and hindered internal rotation (HIR) treatments were also included in the calculations. The results reveal that the ester group (-COO-) selectively promotes the reaction when compared with the traditional hydrocarbon fuels; thus it is recommended that the seven derived rate rules for the title reaction class (including the thermodynamic data of the species involved in the NASA format) should be used for construction of detailed kinetic mechanisms for real biodiesel molecules.


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INTRODUCTION Biodiesel fuels, believed to play an important role in the renewable energy industry, have received much attention for transportation fuel in the 21st century due to exhaustion of fossil fuels. Biodiesels are oxygenated diesel-like fuels consisting of fatty alkyl esters (most commonly fatty acid methyl/ethyl esters) that are derived from vegetable oils and animal fats1-3. Due to the presence of the heterogeneous oxygen atom in the ester functional group (-COO-), physical and chemical properties of biodiesels are different from those of traditional hydrocarbon fuels. Therefore, the use of biodiesels, either as alternative fuels or blends, certainly has an impact on the performance as well as emissions of engines, especially at low temperatures (i.e., T < 1000 K) where the fuel ignition behavior plays an important role. The complexity of biodiesel and the size of its constituent molecules, however, lead to challenges in both direct experimental and detailed kinetic modeling studies. To overcome the barriers, simpler molecules, which have similar chemical functional groups (e.g., methyl/ethyl esters), are used as surrogate fuels. Surrogates are typically used to emulate the physical and chemical properties of real conventional fuels that are too complicated for detailed investigation. Many investigations have been performed to study combustion-related processes of surrogate-biodiesel molecules, most of which are saturated methyl ester and ethyl esters4-10. Currently, there are some studies (e.g., Lai et al., 20115, 9; Wang et al., 201511-12; Zhang et al., 201513; Das et al., 201514; Lin et al.10, 2016; and Kumar et al., 201615) in which theoretical mechanisms for biodiesel combustion have been developed. However, in those mechanisms, the rate assignment, which is based on limited sets of available rate constants, have certainly introduced considerable uncertainty to the rate constants. Recently, computational chemistry has been considering as an effective tool to reliably predict thermodynamic and kinetic data with an accuracy that is generally comparable to the 3 ACS Paragon Plus Environment


experimental studies. Rate estimation rules, thus, can be feasibly obtained now by systematically calculating rate constants for a given reaction class using a test set of small-to-intermediate sized reactants that have the same reaction moiety but different substituents16-21. Thus, there is an opportunity to verify as well as improve the accuracy of previous assignments. Low-temperature combustion, which has potential to improve engine efficiency and reduce toxic emissions, has received much attention in developing oxidation of biodiesel surrogate systems4,

6-9

. All these studies pointed out that mechanisms and kinetics of low

temperature oxidation of biodiesel only involve around a few crucial reaction channels such as: (i) alkyl methyl/ethyl ester peroxy (RO2●) radicals: dissociation (RO2● → R● + O2), concerted elimination (RO2● → ester-olefin + HO2), and isomerization to form the hydroperoxy alkyl methyl/ethyl ester radical (RO2● → ●ROOH); and (ii) hydroperoxy alkyl methyl/ethyl ester (●ROOH) radicals: β-scission to form olefin ester and HO2 (●ROOH → olefin ester + HO2), ketone/aldehyde ester formation (●ROOH → ketone/aldehyde ester+ OH), and cyclic-ether ester formation (●ROOH → cyclic ether/ester + OH)22-23 (cf. Figure 1 for a summary of these important channels). At low temperatures (e.g., < 600 K), RO2● radicals preferably react via concerted elimination and/or isomerization. The concerted elimination channel is believed to inhibit ignition because it produces the relatively unreactive HO2 radical, whereas the isomerization channel may lead to chain branching reactions through the subsequent reactions of the hydroperoxy alkyl radical (β-scission, cyclization and isomerization of ●ROOH). As the temperature increases, dissociation of the alkyl methyl/ethyl ester peroxy radicals becomes more important; this reversibility is linked to the characteristic negative temperature coefficient (NTC) behavior22-23. In recent years, the concerted HO2 elimination channel was also demonstrated as


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one of the most important channels in the combustion mechanisms of alkyl18, 24, ester8-9, 25 and alcohol26.

Figure 1. Potential energy diagram describing the unimolecular reaction channels of (i) RO2● radicals: dissociation back to the reactants, concerted elimination to form olefin and HO2, isomerization to form hydroperoxy alkyl methyl/ethyl ester radicals; and (ii) ●ROOH radicals: βscission to form olefin and HO2, cyclization to cyclic ether/ester formation and OH. “*” denotes the energized molecules. In this study, we present the derivation of the rate estimation rules for the concerted elimination channels for alkyl methyl/ethyl ester peroxy (RO2●), an important reaction type in retarding auto-ignition in the combustion of biodiesel; thus it should be included in any detailed kinetic mechanisms for the parent fuel molecule26. Obtained from the canonical transition state theory (TST) calculations with the corrections from hindered internal rotation and tunneling treatment, the individual rate constants of the reactions in the training set for alkyl methyl/ethyl ester peroxy radicals were used as the basis to develop rate estimate rules for the concerted elimination reactions of ester peroxy radicals.



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COMPUTATIONAL DETAILS The geometry optimizations and electronic energy calculations were performed with the Gaussian 09 computational package27. The composite CBS-QB3 method by Petersson and coworkers28 was selected because of its capability of predicting thermodynamic properties to “chemical accuracy”, which is normally defined as within ̴ 1 kcal/mol of experimental data29. The CBS-QB3 method calculates geometries and frequencies at the B3LYP/6-311G(2d,d,p) level of theory. The vibration frequencies were scaled by a factor of 0.99 for the B3LYP/6311G(2d,d,p) level of theory. The energy is calculated at several levels of theory including CCSD(T)/6-31+G(d’) and then extrapolated to the complete basis set limit. It is worth mentioning that the method has shown to be the effective method for analogous methyl acetate (MA)/methyl propanoate (MP) radicals + O27-8 and alkyl + O2 systems24,

30

. Moreover, the

method was also intensively used to study thermodynamics and kinetics of similar and/or larger oxygenated systems. For example, CBS-QB3 data were used to derive group additive values for different oxygenated compounds31; bond dissociation energies and enthalpies of formation of methyl/ethyl butanoate32; oxidation of methyl and ethyl butanoates33; and abstraction reaction between MA and hydroxyl radical34 in which CBS-QB3 is the method of choice to refine the energy for the use of other methods such as BH&HLYP35-36 and MP237. A good agreement betwween the CBSQB3 and G3MP2B338 levels on calculated reaction barriers and energies for several selected reactions were also observed (cf. Table S2). All reported results for stable molecules as well as transition states (first-order saddle points on the PESs) were obtained with the lowest-energy conformer of a given species. The normal-mode analysis was performed to verify the nature of stationary structures. The minimum energy paths (MEP) from the transition


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state to the corresponding reactants and products were carried out using the intrinsic reaction path (IRC) following method39-40. The standard enthalpies of formation ( ∆ f H o ) of the species involved were calculated using the atomization energy method41. Entropies (S) and heat capacities (Cp) of each molecule were obtained within the statistical thermodynamic framework42. Because only relative energies are required in this work, no attempts were made to improve the heats of formation using, for example, bond additivity corrections as well as other methods such as the isodesmic reaction procedure. All harmonic frequencies were scaled by a factor of 0.99 as recommended by Petersson and coworkers28 prior to their use. In order to improve the results, some low-frequency vibrational modes were treated as internal rotations (e.g., the rotation of alkyl and OH groups around single bonds C-C and C-O). The corresponding hindrance potentials were obtained at the B3LYP/6-31G(d) level of theory via relaxed surface scans with a step size of 10°. Reduced moments of inertia for asymmetric internal rotors were calculated at the I(2,3) level based on the equilibrium geometry as defined by East and Radom43. The 1-D Schroedinger equation was then numerically solved for each internal rotor using the eigenfunctions of the 1-D free rotor as basis functions. The energy eigenvalues were then used to numerically calculate their contributions to thermodynamic functions by an explicit evaluation of the hindered rotations as described in our previous work7-8. All thermodynamic and high-pressure rate coefficient calculations were carried out using the Multi-Species Multi-Channel (MSMC) code44-46. Tunneling correction factors were calculated with asymmetric Eckart potential methods47. Rate constants calculated for the temperature range of 300 - 2000 K in steps of 50 K were fitted to a modified Arrhenius



expression: k(T) = n H × A H × T n × exp(-E/RT) , where n H is the number of equivalent hydrogen atoms, A H is the pre-exponential factor expressed on a per hydrogen-atom basis, n is the temperature exponent, and E is a parameter related to the activation energy in the original Arrhenius expression. Rate estimation rules derived in this work were obtained by least-squares minimization to averaged data of the individual rate constants within a given reaction class at each temperature from 300 to 2000 K with the increment of 50 K and then fitting these averaged values to sets of three modified Arrhenius parameters ( A H , n, E). Similar to the rate rule derivation for the alkyl + O2 system, the uncertainty in the calculated rate constants is estimated to be approximately a factor of 2 at 1000 K16, 18, 48-49, respectively. This uncertainty arises from errors in the ab initio method (i.e., CBS-QB3), such as variations in optimized reactant/product (the lowest energy-lying conformers were chosen) and TS geometries as well as errors in the harmonic frequencies (including the scaling factor) and hindered internal rotors calculations50. It is expected that the rate rules, derived from the averaged values for each class, will have the similar uncertainty (i.e., a factor of 2 at 1000 K)16, 18-20, 50.

RESULTS AND DISCUSSION In this section, we present the rate rule derivation for the concerted elimination reaction of RO2●, where R is the biodiesel radical. The rate rules were developed from a set of reactions that consist of all possible alkyl methyl/ethyl ester peroxy radicals whose parent biodiesel molecules were listed in Figure 2. The results were then validated with available data as well as compared with the previously reported values of the analogous hydrocarbon systems to investigate the effects of the ester (–COO–) and alkyl groups on the kinetic behaviors, from which specific rate rules were proposed. 8 ACS Paragon Plus Environment

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Figure 2. Parent biodiesel surrogate molecules (straight and branched alkyl chains) considered in this study.

A typical HO2 concerted reaction proceeds via a planar five-membered ring transition state (cf. Scheme 1) with the breaking of the C–OO, C–H bonds and formation of OO–H bond simultaneously. Because the dissociation energy is sensitive to the intrinsic structure of the RO2● radical11, 51-53, it is expected that the considered reactions require a detailed classification in terms of the nature of the peroxy moiety and the type of the broken C–H bond.



Reactant (RO2●)

5-membered-ring TS

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Products

Scheme 1. Reaction scheme for the concerted HO2 elimination with the corresponding broken C–OO/C–H bonds and formed OO–H/C=C bonds. R1, R2, R3 and R4 can be hydrogen and/or (ester-) alkyl groups. To facilitate the classification, the notation for the reaction type, which depends on the nature and the position of the carbon site relative to the ester group, was introduced as follows •

nature of C site nature of C site OOposition of C site relative to -COO- group − Hposition of C site relative to -COO- group

(1)

The nature of the carbon site (either connecting to the active OO group or H atom) can be primary, secondary or tertiary (denoted as “p”, “s” and “t”, respectively); and the position (or location) of the carbon site relative to the ester (–COO–) group can be α, β, γ, δ, σ, x or y carbon sites (cf.

Figure 3). For example,

OOαs − Hβp means that the OO group connects to the

secondary carbon at the α position and the abstracted H atom connects to the primary carbon at the β position. In other words, the notation is for the following reaction (H atoms are not explicitly presented if not relevant to the reaction).

(2)


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Figure 3. Carbon site labels used in this work, relative to the ester group. “R”, “ester” and “R’” denote the C1-C4 alkyl chain (straight or branched), –COO– and CH3/C2H5 groups, respectively.

Thermodynamic properties calculation Table 1 presented the calculated thermodynamic properties (∆fH298, S298 and

CTp ) for

several selected species. The data for all species involved in this study can be found in the accompanied supplementary materials. It is observed that the calculated numbers are in good agreement with the literature values suggested by Tao and Lin9, Fisher et al.3 and Herbinet et al. 54

(the corresponding mean absolute deviation (MAD) values are 0.7, 0.7 and 0.9 kcal/mol for

∆fH298). Although our ∆fH298 values are close to those estimated by Wang and Zhang11 (MAD = 0.6 kcal/mol), the calculated numbers for S298 and

C300 are considerably different from those p

suggested by those authors. These discrepancies are likely due to the more rigorous framework used in our methodology (c.f. “Computational Details”). Overall, the good agreement between the present and the previous studies gives us confidence on our calculated thermodynamic data which were then used to calculate high-pressure rate constants for the reactions in the training set.




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Table 1: Comparison of Calculated Thermodynamic Properties with Literature Data: This work[a], Tao[b], Fisher[c], Herbinet[d] and Wang[e]. Units: kcal/mol for △fH298 and cal/mol-K for S298 and CpT. Species

CC=C-COO-C

C=CC-COO-C

C=C-COO-C

CCC(OOH)-COO-C

CC(OOH)C-COO-C

C(OOH)CC-COO-C

Method

△fH298 [f]

S298

Cp298

Cp300

Cp400

Cp500

Cp600

Cp800

Cp1000

Cp1500

This work

-82.4

90.8

30.0

30.1

36.5

42.4

47.6

55.8

61.8

70.7

Tao

-82.3

87.7

29.3

29.5

36.5

42.7

48.0

56.5

62.8

72.3

Fisher

-82.0

94.0

31.0

-

-

-

-

-

-

-

Herbinet

-84.0

94.0

31.0

-

-

-

-

-

-

-

This work

-77.7

93.0

29.5

29.6

36.0

41.9

47.0

55.1

61.0

70.0

Tao

-78.1

90.3

29.1

Fisher

-76.0

92.0

30.0

29.3 -

36.5 -

42.8 -

48.2 -

56.7 -

62.9 -

72.4 -

Herbinet

-76.0

89.0

30.0

-

-

-

-

-

-

-

This work

-73.8

81.2

24.2

24.3

29.6

34.5

38.7

45.1

49.7

56.5

Tao

-73.6

79.7

24.0

Fisher

85.0 85.0

26.0

29.8 -

34.7 -

38.8 -

45.4 -

50.2 -

57.5 -

Herbinet

-74.0 -74.0

24.1 -

25.0

-

-

-

-

-

-

-

This work

-94.3

109.5

37.9

38.1

46.0

53.1

59.1

68.3

75.0

85.0

Tao

-92.0

107.6

37.2

Fisher

-95.0

109.0

40.0

37.4 -

46.0 -

53.3 -

59.6 -

69.6 -

76.8 -

87.6 -

Herbinet

-95.0

109.0

40.0

-

-

-

-

-

-

-

This work

-98.6

107.1

38.1

38.2

46.0

53.1

59.1

68.4

75.1

85.4

Tao

-97.0

106.1

37.2

Fisher

-99.0

110.0

39.0

37.3 -

45.8 -

53.1 -

59.4 -

69.4 -

76.7 -

87.5 -

Herbinet

-98.0

110.0

39.0

-

-

-

-

-

-

-

This work

-95.5

109.1

40.5

40.6

48.2

54.9

60.4

69.1

75.4

85.1

Tao

-95.0

105.4

36.0

Fisher

-94.0

112.0

39.0

36.1 -

44.9 -

52.5 -

58.9 -

69.1 -

76.5 -

87.4 -

Herbinet

-94.0

112.0

39.0

-

-

-

-

-

-

-


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Species CCC=C-COO-C

CC(C)=C-COO-C CC=CC-COO-C CC=C(C)-COO-C CC(=C)C-COO-C C=CCC-COO-C

HO2

[a]

Method

△fH298 [f]

S298

Cp298

Cp300

Cp400

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Cp500

Cp600

Cp800

Cp1000

Cp1500

This work

-86.7

100.0

35.2

35.3

43.3

50.6

56.9

66.8

74.0

84.8

Wang

-86.1

101.4

-

39.8

47.2

54.1

60.1

69.9

77.3

87.8

This work

-90.0 -89.2

97.1 106.9

34.9 -

35.1 40.9

43.3 48.2

50.7 54.9

57.0 60.7

66.7 70.3

73.8 77.4

84.6 87.7

-85.1 -84.6

101.9 104.5

34.8 -

35.0 38.6

42.5 45.8

49.6 52.5

55.7 58.6

65.6 68.5

72.9 75.9

84.0 86.8

-88.3 -88.3

99.6 111.8

33.5 -

33.7 39.6

41.6 46.6

49.1 53.2

55.6 59.1

65.8 68.7

73.2 75.9

84.4 86.9

Wang

-86.2 -84.6

101.3 108.5

34.9 -

35.0 40.5

42.6 47.1

49.7 53.4

55.9 59.1

65.7 68.5

72.9 75.7

84.1 86.3

This work

-83.3

100.4

34.7

35.3

43.1

50.3

56.7

66.9

74.5

85.7

Wang

-82.9

109.3

-

40.6

47.3

53.7

59.4

68.8

75.9

86.5

This work

2.1

54.8

8.3

8.3

8.8

9.4

9.9

10.7

11.3

12.3

Tao

3.0

54.7

8.3

Fisher

4.0

55.0

8.0

8.3 -

8.8 -

9.3 -

9.8 -

10.6 -

11.3 -

12.3 -

Herbinet

3.0

55.0

8.0

-

-

-

-

-

-

Wang This work Wang This work Wang This work

Obtained at CBS-QB3 level of theory; atomization method;

[b]

9 [c]

Suggested by Tao et al. ;

3 [d]

Fisher et al. ;


54 [e]

Herbinet et al. ;

11 [f]

Wang et al. ;

Calculated using the

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Rate Constant Calculations The calculated high-pressure rate constants of the reactions involving the considered biodiesel radicals were used as the basis to derive the rate rules for the concerted HO2 elimination reaction class. With the criterion of having the uncertainty of two for the derived calculated rates, the HO2 elimination reactions in the training set were partitioned into seven main classes, namely

C=x , Cα= −high(β -α ) , Cα= − high(α − β ) , Cα= − low(cis ) , Cα= −low(trans) , C=β and Cγ= .

For the reactions at Cα site, due to the significant effects of the neighboring substituents, the =

= = classes Cα − high and Cα − low were proposed for the formation of (i) either tri- or tetra-

substituted olefin products (“highly-substituted” for short) and (ii) the other olefins (or “lowly-substituted”), respectively. This notation was adopted from analogous alkyl peroxy radicals where the different behaviors of the reactions leading to lowly and highly substituted olefins were observed.18 Also, in order to achieve the expected uncertainty of two for the =

=

=

= = = derived calculated rates, Cα − high were subclassified as Cα −high(β -α ) and Cα − high(α − β ) ; and = = Cα= − low were further divided into Cα − low(cis ) and Cα − low ( trans ) (due to the existence of the

cis- and trans- conformers of the transition states). The summary of the rate rule classification with the detailed and simplified reaction notations was presented in Table 2.



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Table 2: Summary of Rate Rule Classification. Location of the C=C bond of the product olefin

Cx

Rate rule class

C =x

position

=

Cα −high(β -α )

Cα position & highly-substituted olefinb

Cα

Cα= − high(α − β )

Cα= − low ( cis )

position

& lowly-substituted olefinb

Cα= − low ( trans )

Reaction type Detailed notationa Simplified notation

OOsx - Hyp

OOx - H y

OOyp - Hsx

OOy - Hx

(OObs (OOtb (OOta (OOas (OOas (OOas (OOta (OObp (OO bs (OObp (OOas (OObs -

H ta )

high

)high H bs ) high t Hb ) high p Hb ) low ( cis ) s Hb ) low ( cis ) p Hb ) low ( cis ) s Ha ) low ( cis ) s Ha ) low ( cis ) t Ha ) low ( cis ) s Hb ) low( trans ) s Ha ) low( trans ) H as

(OOb - Ha )high (OOa - Hb )high (OOa -

Hb )

(OO b -

Ha )

(OO a (OO b -

Hb )

low ( cis )

low ( cis )

low ( trans )

Ha )

low ( trans )

OObs - Hgp OObs - Hgs OOtb - Hgp

=

Cβ position

OOb - Hg

Cβ

OOgp - Hbs OOgp - Htb

OOg - Hb

OOgs - Hbs =

Cγ position

a

Detailed reaction-type notation:

Cγ

•

OOsg - Hdp

OOg - Hd

OOdp - Hgs

OOd - Hg

nature of C site nature of C site OOposition of C site relative to ester group − Hposition of C site relative to ester group . See

the main text for the description. “highly-substituted olefin” denotes either tri- or tetra-substituted olefin. The other olefins are classified as “lowly-substituted olefin”. b


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i) Class

C=x : the C=C bond of the product olefin at C x .

In this class, the double bond is formed at C x site due to (i) the abstraction of hydrogen on Cy and the breaking of C–OO bond on C x or (ii) the abstraction of hydrogen at C x and the breaking of C–OO bond at C y . The detailed reaction-type notations for the two cases are

OOsx −Hyp and OOyp −Hsx , respectively (cf. Scheme 2).

Scheme 2. Reaction scheme for class

C=x , leading to an alkyl-ester olefin whose double bond

is at C x . The reaction types were given in parentheses. The calculated rate constants (in the modified Arrhenius format) on a per H-atom basis for reactions in this class were provided in Table 3. The ratios of the TST rate constants to the corresponding rate-rule-derived numbers (cf. Computational Details for the rate rule derivation) at 600, 800 and 1000 K as well as the reaction enthalpy ( ∆Hrxn ) and entropy ( ∆Srxn ) at 298 K were also provided. It is observed that the alkyl (R) structure (in terms of length/branch) slightly affects the reactivity on the ethyl moiety. Similar to the results reported by Wang for the H-abstraction from an ethyl ester with hydrogen radicals52, the rate p

s

constants of the H-abstraction reactions from C x site ( OOy −Hx ) are twice as fast as those s

p

from the C y site ( OOx −Hy ) at 800 K. Since the difference between the two sites is quite small and for simplicity, the average rate constants were used for all reactions (denoted as 17 ACS Paragon Plus Environment


Class

Page 18 of 45

C=x ). The simplification introduced the average factor of ~1.1 times to the explicitly

calculated rate constants at 800 K. It was also found that the ester group inhibits the title reaction when compared to the hydrocarbon fuels. For instance, the rate constants of the ester peroxy are about 3 - 13 times slower than those of ethyl peroxy (C2H5OO●)

18, 30

and the

difference is more noticeable at low temperature (i.e., < 1000 K). The differences between biodiesel and hydrocarbon systems were further discussed in the last session of this manuscript.


Page 19 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 3. Fitting Modified Arrhenius Parameters on a per H-atom basis, Enthalpies and Entropies for Reactions Used to Derive Rate Rules for Class

No.

C=x .

Reaction R-COO-R’Q● → Ester olefins + HO2

C=x 1

C-COO-CQ●C→C-COO-C=C + HO2

Type & Location of No. C-OO site C-H site of H 1

Modified Arrh. Parameter n E -1

298

∆rxnH -1

[s ]

k TST/k rate rule

Thermochemistry

AH

[kcal mol ]

-1

∆rxnS

298

-1

-1

[kcal mol ] [cal mol K ]

600 K 800 K 1000 K

4.20E+05

2.08

29.69

3

s, x

p, y

3.43E+05

2.17

29.43

24.51

35.47

(1.12) (1.11) 0.61

0.59

(1.10) 0.58

p, y

2

CC-COO-CQ●C→CC-COO-C=C + HO2

3

s, x

1.58E+04

2.62

29.01

24.63

36.00

0.70

0.71

0.74

3

CCC-COO-CQ●C→CCC-COO-C=C + HO2

3

s, x

p, y

1.54E+04

2.62

29.03

24.70

34.93

0.68

0.70

0.72

4

CCCC-COO-CQ●C→CCCC-COO-C=C + HO2

3

s, x

p, y

1.23E+04

2.61

29.01

24.73

35.15

0.54

0.55

0.57

5

C2 C-COO-CQ●C→C2 C-COO-C=C + HO2

3

s, x

p, y

5.81E+05

2.16

29.29

24.75

36.52

1.09

1.03

1.00

6

C2 CC-COO-CQ●C→C2 CC-COO-C=C + HO2

3

s, x

p, y

1.01E+04

2.71

29.05

25.03

35.84

0.78

0.81

0.87

7

C-COO-CCQ●→C-COO-C=C + HO2

2

p, y

s, x

3.17E+07

1.61

30.31

17.81

34.50

1.12

1.11

1.08

8

CC-COO-CCQ●→CC-COO-C=C + HO2

2

p, y

s, x

3.39E+07

1.62

30.23

17.82

34.66

1.35

1.33

1.28

9

CCC-COO-CCQ●→CCC-COO-C=C + HO2

2

p, y

s, x

3.97E+07

1.61

30.25

17.90

34.09

1.54

1.52

1.47

10 CCCC-COO-CCQ●→CCCC-COO-C=C + HO2

2

p, y

s, x

2.12E+06

1.95

30.13

17.90

32.18

0.81

0.85

0.88

11 C2 C-COO-CCQ●→C2 C-COO-C=C + HO2

2

p, y

s, x

4.04E+07

1.62

30.38

17.98

34.99

1.48

1.50

1.48

2

p, y

s, x

6.41E+07

1.62

30.17

17.87

35.00

2.69

2.61

2.50

12 C2 CC-COO-CCQ●→C2 CC-COO-C=C + HO2

Hydrogen is not explicitly provided, unless it involves in the considered reactions and/or it is for clarity; the dot “•” symbolizes a radical site; and “p” refers to primary, “s” to secondary, “t” to tertiary. “R”, “R’” and “Q” denote alkyl, methyl/ethyl and -OOH groups, respectively. The values in parentheses are the averaged ratios for the reactions considered.



Page 20 of 45

When the double bond was formed at Cα site, due to the difference in the kinetic behaviors, the reactions were divided into two classes; namely, the products are (i) either tri- or tetra-substituted olefins (denoted as highly-substituted) and (ii) the other olefins (denoted as =

= “lowly-substituted”). The former class was further divided into two subclasses, Cα −high(β -α ) and

Cα= − high(α − β ) , due to the sensitivity of the reaction rate on the position of the OO group and the =

=

= = abstracted H atom ( Cα −high(OO position -H position) ). The latter was classified as Cα−low(cis) and

Cα= −low(trans ) due to the difference between the cis- and trans-conformers of the product alkene. Note that the classification was adopted from the previous study for the rate rules on alkyl peroxy radicals18. =

= ii) Class Cα −high(β -α ) : the highly-substituted olefin formed via the

OOβ −Hα reaction and its

C=C bond at Cα . In this class, the product is either tri- or tetra-substituted olefin with the double bond at

Cα site due to the breaking of the C–OO bond on C β and the abstraction of hydrogen at Cα . The possible reactions are

OOsβ − Hαt or OOtβ − Hαs (cf. Scheme 3)


Page 21 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


=

= Scheme 3. Reaction scheme for class Cα−high , leading to either a tri- or tetra-substituted (or

highly-substituted) olefin whose double bond is at Cα . The reactions were divided into two =

=

= = subclasses, Cα −high(β -α ) and Cα − high(α − β ) (see main text for detailed description). The reaction

types were given in parentheses. =

= The calculated TST and the derived rate rules for the Cα −high(β -α ) class as well as the

thermochemistry for the considered reactions were provided in Table 4. The rate rule (in the modified Arrhenius format) on a per H-atom basis was derived for the temperature range of 300 – 2000 K as follows

kα -high( β −α ) (T) = 1.48 × 109 × T1.02 × e

-12979 T

=

= iii) Class Cα − high(α − β ) : the highly-substituted olefin formed via the

C=C bond at Cα


[s-1]

(3)

OOα −Hβ reaction and its


Page 22 of 45

In this class, the product is either a tri- or tetra-substituted olefin with the double bond at

Cα site due to the Cα − OO breaking and the H abstraction at C β . The possible reactions are

OOαs − Htβ or OOαt − Hsβ (cf. Scheme 4, lower scheme). The calculated TST values and the =

= derived rate rules for the Cα −high(α −β ) class as well as the thermochemistry for the considered

reactions were also provided in Table 4. The derived rate rule, provided in the modified Arrhenius format, on a per H-atom basis for the temperature range of 300 – 2000 K is

kα -high(α −β ) (T) = 9.06 × 107 × T1.30× e

-13326 T

[s-1]

(4)

In the considered temperature range of 300 – 2000 K, the rate rules indicate that the

Cα= −high(β -α ) reactions are faster than Cα= −high(α −β ) reactions by a factor of 2 – 10.5 (as shown in Table 4). It is likely that this deviation is subject to the effect of the ester group on the breakage of

C− H

bonds

on

the

different


carbon

sites.

Page 23 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 4. Fitting Modified Arrhenius Parameters on a per H-atom Basis, Enthalpies and Entropies of Reactions Used to Derive =

= Rate Rules for Class Cα−high .

No.

Reaction ●QR-COO-R’ → Ester olefins + HO2

Type & Location of No. C-OO site C-H site of H


298

∆rxnH -1

[s ]

k TST/k rate rule

Thermochemistry

AH

[kcal mol ]

-1

∆rxnS

298

-1

-1


600 K 800 K 1000 K

Cα= − high Cα= −high(β -α )

1

1.48E+09

1.02

25.79

(1.01) (1.02) (1.02)

1 C2 CQ●C-COO-C→C2 C=C-COO-C + HO2

2

t, β

s, α

4.42E+09

0.92

25.75

21.30

38.15

0.80

0.77

0.75

2 C2 CQ●C-COO-CC→C2 C=C-COO-CC + HO2

2

t, β

s, α

9.40E+08

1.26

26.09

21.76

38.27

1.10

1.26

1.38

3 CCQ●C(C)-COO-C→CC=C(C)-COO-C + HO2

1

s, β

t, α

8.11E+08

1.09

25.60

18.13

40.15

1.02

1.00

1.00

4 CCQ●C(C)-COO-CC→CC=C(C)-COO-CC + HO2

1

s, β

t, α

5.70E+09

0.82

25.71

18.38

40.00

1.11

1.03

0.97

9.06E+07

1.30

26.48

=

Cα − high(α − β )

1

(1.09) (1.09) (1.08)

1 C2 CCQ●-COO-C→C2 C=C-COO-C + HO2

1

s, α

t, β

1.13E+07

1.52

26.25

13.15

34.47

0.59

0.60

0.61

2 C2 CCQ●-COO-CC→C2 C=C-COO-CC + HO2

1

s, α

t, β

3.36E+07

1.42

26.41

13.51

34.94

0.83

0.84

0.86

3 CCCQ●(C)-COO-C→CC=C(C)-COO-C + HO2

2

t, α

s, β

6.21E+08

1.15

26.63

17.04

38.93

1.10

1.08

1.06

2

t, α

s, β

1.17E+09

1.13

26.63

17.45

39.38

1.86

1.82

1.79

4 CCCQ●(C)-COO-CC→CC=C(C)-COO-CC + HO2

See the footnote of Table 3 for notation description.



Page 24 of 45

=

= iv) Class Cα − low ( cis ) : the lowly-substituted cis olefin formed and its C=C bond at Cα

The product in this class is not a tri- or tetra-substituted olefin and has the double bond at

Cα site due to (i) the breaking of C–OO bond on Cα and the abstraction of hydrogen on C β (three possible cases are

OOαs −Hβp , OOαs −Hsβ or OOαt −Hβp ) or (ii) the breaking of C–OO bond p

s

on C β and the abstraction of hydrogen on Cα ( OOβ −Hα ,

OOβp −Hαt or OOsβ −Hαs ) (cf. Scheme

4). Table 5 presented the calculated TST rate constants for reactions in this class and the rate rule (in the modified Arrhenius format on a per H-atom basis) derived for the temperature range of 300 – 2000 K as follows

k α −low( cis ) (T) = 5.10 × 106 × T1.64 × e

-12840 T

[s-1]

(3)

= Scheme 4. Reaction scheme for class Cα − low , leading to a lowly-substituted alkyl-ester olefin

whose double bond is at Cα site. The reaction types were given in parentheses.


Page 25 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


=

= v) Class Cα −low( trans ) : the lowly-substituted trans olefin formed and its C=C bond at Cα

The two reaction types in this class are (OOas - H bs )

low ( trans )

and (OO bs - H as )

low ( trans )

. This

=

= class is similar to the previous class Cα−low(cis) except that the olefin is the trans-conformer. The

reaction scheme for this class was illustrated in Scheme 4. The rate rule on a per H-atom basis was derived for the temperature range of 300 – 2000 K as follows

kα −low(trans ) (T) = 3.68 × 107 × T1.50 × e

-12227 T

[s-1]

(4)

=

= The classification of the cis and trans conformer olefins in the two classes, Cα−low(cis) and

Cα= −low(trans ) , is due to the difference of the transition state types (i.e., cis- vs. trans- structures). Because the trans-TS is about 2 kcal/mol lower than the cis-TS (cf. Figure 4 for CCCQ●–COO– CC → CC=C–COO–CC + HO2 reactions), the trans channel occurs much faster (cf. Table 4). For example, the trans-TS is about 2.1 kcal/mol lower than the cis-TS for CCCQ●–COO–CC → CC=C–COO–CC + HO2 reactions; thus the former reaction occurs about 7.2 and 3.6 times faster at 600 K and 1000 K (see Figure 5 and Table 4) to form the corresponding olefins, respectively. In general, the reaction via the trans-TS is about 8.1 and 5.0 times faster at 600 K and 800 K, respectively; therefore, the trans-TS channel, compared to the cis channel, is expected to play a more important role in low-temperature chemistry in engine combustion.



Page 26 of 45

cis- TS E(kcal/mol)

27.92

+

25.82 15.50 13.70 0.00

+

trans- TS

Figure 4. Potential energy surface of the reaction CCCQ●–COO–CC → CC=C–COO–CC + HO2 via cis and trans TSs to form the corresponding cis- and trans- olefins at 0 K, respectively.

Figure 5. Comparison of the rate constants of the reaction CCCQ●–COO–CC → CC=C–COO– CC + HO2 via cis- and trans- transition states. See Table 2 for the reaction type notation.


Page 27 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


It is shown in Table 5 that the methyl/ethyl groups do not affect the rate of the reactions leading to the double bond formed at Cα . In particular, the rate-constant ratios of the methyl to ethyl systems (e.g., reactions 1 and 2) are about 0.97 and 1.05 at 600 and 1000 K, respectively. =

=

= = In general, the rate constants for Cα−low(cis) and Cα −low( trans ) can be estimated by the derived rate

rule within a factor of 2 when compared to the explicitly calculated values.


The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

Page 28 of 45

Table 5. Fitting Modified Arrhenius parameters on a per H-atom Basis, Enthalpies and Entropies of Reactions Used to Derive Rate Rules for Class

Cα= −low .

Reaction

No.

●QR-COO-R’ → Ester olefins + HO2



298

∆rxnH -1

[s ]

k TST/k rate rule

Thermochemistry

AH

[kcal mol ]

-1

∆rxnS

298

-1

-1

600 K

800 K

1000 K


Cα= − low Cα= − low ( cis )

5.10E+06

1.64

25.51

(1.03)

(1.02)

(1.02)

1

CCQ●-COO-C→C=C-COO-C + HO2

1 3

s, α

p, β

9.86E+05

2.04

24.90

17.62

34.52

1.40

1.38

1.40

2

CCQ●-COO-CC→C=C-COO-CC + HO2

3

s, α

p, β

9.45E+05

2.05

24.88

17.75

35.54

1.44

1.42

1.44

3a CCCQ●-COO-C→CC=C-COO-C + HO2 (cis )

2

s, α

s, β

1.75E+07

1.60

25.97

15.55

34.24

0.89

0.97

1.02

4a CCCQ●-COO-CC→CC=C-COO-CC + HO2 (cis )

2

s, α

s, β

2.33E+07

1.57

26.07

15.90

34.04

0.95

1.04

1.10

5a CCCCQ●-COO-C→CCC=C-COO-C +HO2 (cis )

2

s, α

s, β

3.88E+06

1.77

25.08

15.78

34.19

1.28

1.21

1.18

6a CCCCQ●-COO-CC→CCC=C-COO-CC +HO2 (cis )

2

s, α

s, β

2.91E+06

1.78

25.42

16.21

33.89

0.78

0.79

0.81

7

C2 CQ●-COO-C →C=C(C)-COO-C + HO2

6

t, α

p, β/β'

1.32E+07

1.67

24.84

19.59

36.90

0.91

0.80

0.74

8

C2 CQ●-COO-CC →C=C(C)-COO-CC + HO2

6

t, α

p, β/β'

1.63E+07

1.66

24.92

19.82

37.24

0.99

0.88

0.82

9

CQ●C-COO-C→ C=C-COO-C + HO2

2

p, β

s, α

3.78E+05

2.02

24.50

18.16

32.89

0.99

0.89

0.85

10 CQ●C-COO-CC→C=C-COO-CC + HO2

2

p, β

s, α

3.88E+05

2.01

24.54

18.19

33.85

0.93

0.84

0.81

11a CCQ●C-COO-C→CC=C-COO-C + HO2 (cis )

2

s, β

s, α

3.81E+09

0.84

27.07

21.09

35.37

0.61

0.67

0.68

12a CCQ●C-COO-CC→CC=C-COO-CC + HO2 (cis )

2

s, β

s, α

3.82E+07

1.57

26.85

21.38

35.43

0.79

1.02

1.19

13a CCCQ●C-COO-C→CCC=C-COO-C + HO2 (cis )

2

s, β

s, α

8.14E+07

1.40

26.19

21.43

36.23

0.99

1.07

1.10

14a CCCQ●C-COO-CC→CCC=C-COO-CC + HO2 (cis )

2

s, β

s, α

8.49E+07

1.37

26.25

21.57

35.86

0.83

0.90

0.93

15 CQ●C(C)-COO-C →C=C(C)-COO-C + HO2

1

p, β

t, α

2.32E+07

1.43

25.38

16.29

36.08

1.39

1.28

1.20

16 CQ●C(C)-COO-CC →C=C(C)-COO-CC + HO2

1

p, β

t, α

2.20E+07

1.43

25.36

16.34

35.97

1.31

1.19

1.12

3.68E+07

1.50

24.30

(1.06)

(1.05)

(1.05)

=

Cα − low ( trans )

1

3b CCCQ●-COO-C→CC=C-COO-C + HO2 (trans )

2

s, α

s, β

2.19E+07

1.62

23.91

13.89

36.15

0.91

0.87

0.85

4b CCCQ●-COO-CC→CC=C-COO-CC + HO2 (trans )

2

s, α

s, β

2.61E+07

1.59

23.99

14.16

34.46

0.85

0.81

0.80

5b CCCCQ●-COO-C→CCC=C-COO-C + HO2 (trans )

2

s, α

s, β

2.76E+07

1.61

23.43

14.06

36.54

1.60

1.38

1.27

6b CCCCQ●-COO-CC→CCC=C-COO-CC + HO2 (trans )

2

s, α

s, β

2.89E+07

1.61

23.75

14.56

35.40

1.28

1.17

1.12

11b CCQ●C-COO-C→CC=C-COO-C + HO2 (trans )

2

s, β

s, α

6.54E+07

1.58

24.64

19.24

38.48

1.10

1.21

1.29

12b CCQ●C-COO-CC→CC=C-COO-CC + HO2 (trans )

2

s, β

s, α

7.85E+07

1.59

24.60

19.26

37.09

1.47

1.61

1.70

13b CCCQ●C-COO-C→CCC=C-COO-C + HO2 (trans )

2

s, β

s, α

6.14E+08

1.20

24.98

19.71

38.59

0.71

0.75

0.77

14b CCCQ●C-COO-CC→CCC=C-COO-CC + HO2 (trans )

2

s, β

s, α

6.04E+08

1.18

25.08

19.92

37.37

0.55

0.59

0.61

See

the

footnote

of

Table

3


for

notation

description.

Page 29 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


=

= vi) Class Cβ : the C=C bond of the product olefin at C β

The double bond can be formed at C β site via the concerted eliminations of H at either Cβ

or C γ . To facilitate the discussion, the 16 reactions (cf. Table 6) were divided into two

groups, namely

OOβ −Hγ (short notation for three possible reactions: OOsβ −Hγp , OOsβ −Hγs and

OOtβ −Hγp ) and OOγ −Hβ ( OOγp −Hsβ , OOγp −Htβ and OOγs −Hsβ ). The detailed reaction mechanism was depicted in Scheme 5 with either trans- and cis- products (if the alkyl chain is long enough) formed.

= Scheme 5. Reaction scheme for class Cβ , leading to an alkyl-ester olefin whose double bond is

at C β . The reaction types were given in parentheses. Similar to the

Cα= −low and Cα=−high classes, we also examined the cis- and trans-TS for the

reaction in this class. For reaction in the first group

OOβ −Hγ (reactions 1-6, Table 6), it is

observed that reaction rates for cis-TS and trans-TS pathway are rather comparable (e.g.,

k(trans) / k(cis) = 1.39 at 600 K) while the rate constant for the trans-TS is slower than the cis-



TS pathway for the reaction in the second group

Page 30 of 45

OOγ −Hβ (e.g., k(trans) / k(cis) = 3.80 at 600

K). The difference between the cis- and trans-TSs can be explained by the location of the reaction site. In other words, the effect of the –COO– (making the difference between the cisand trans- structure) on the rate constants decreases with the distance of the reaction site (e.g., β vs. γ sites). For the rate rule derivation, due to their slow rate, the cis-TS pathways in the second group ( OOγ

− Hβ ) was not included. It is worth mentioning that the difference between

the cis- and trans-TS channels is consistent with the observation in the study on the rate rule of the alkyl peroxy concerted HO2 elimination channel18. The predicted rate constants using the rate rule are very close to the explicitly calculated numbers (e.g., the kTST / krate rule ratio is close to unity in 600 – 1000 K range) except the

OOtβ −Hγp reaction (reactions 5 and 6 in Table 6). To be specific, the kTST / krate rule ratios are about 2.5 and 3.1 times, respectively, for reactions 5 and 6 at 600 K. At this stage, the reason for this deviation is not clear, at least, to us. In addition, it is observed that the methyl and ethyl groups only have a minor effect on the rate constants of reactions in this class as discussed previously. As mentioned above, in comparison with the reactions forming the double bond on the

Cα= class, reactions belonging to class C=β were less affected by the ester group. To be specific, =

= the rate constant of the Cβ class are considerably slower than those on the on the

Cα= class and

the difference is more significant at low temperature. This can be explained by different effects of the double bond of the ester group (i.e., C=O) on different reaction sites in the alkyl group for the hydrogen-abstraction11, and/or it can be caused by the hyperconjugation effect to C−OO bond dissociation55. 30 ACS Paragon Plus Environment

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Table 6. Fitting Modified Arrhenius Parameters on a per H-atom Basis, Enthalpies, and Entropies of Reactions Used to Derive =

= Rate Rules for the Class Cβ .

No.


C=β


Modified Arrh. Parameter n E AH -1

1

298

∆rxnH -1

[s ]

[kcal mol ]

1.80E+09

1.06

29.54

k TST/k rate rule

Thermochemistry -1

∆rxnS

298

-1

-1


600 K 800 K 1000 K (1.15) (1.14) (1.13)

1 CCQ●C-COO-C→C=CC-COO-C + HO2

3

s, β

p, γ

4.35E+07

1.72

29.31

23.90

40.68

0.69

0.79

0.89

2 CCQ●C-COO-CC→C=CC-COO-CC + HO2

3

s, β

p, γ

5.41E+07

1.73

29.23

23.91

40.95

0.96

1.09

1.22

3a CCCQ●C-COO-C→CC=CC-COO-C + HO2 (cis )

2

s, β

s, γ

3.20E+09

1.06

29.65

22.47

40.47

0.84

0.87

0.88

3b CCCQ●C-COO-C→CC=CC-COO-C + HO2 (trans )

2

s, β

s, γ

3.04E+09

1.08

29.23

21.36

40.48

1.27

1.20

1.16

4a CCCQ●C-COO-CC→CC=CC-COO-CC + HO2 (cis )

2

s, β

s, γ

4.24E+09

1.05

29.71

22.62

40.65

0.97

1.00

1.02

4b CCCQ●C-COO-CC→CC=CC-COO-CC + HO2 (trans )

2

s, β

s, γ

3.02E+09

1.08

29.23

21.44

40.11

1.23

1.16

1.12

5 C2CQ●C-COO-C→C=C(C)C-COO-C + HO2

6

t, β

p, γ/γ'

1.19E+11

0.77

29.11

25.14

42.42

2.51

2.11

1.88

6 C2CQ●C-COO-CC→C=C(C)C-COO-CC + HO2

6

t, β

p, γ/γ'

2.98E+10

1.07

29.55

25.26

41.74

3.06

3.08

3.09

7 CQ●CC-COO-C→C=CC-COO-C + HO2

2

p, γ

s, β

3.41E+09

1.04

29.69

20.80

38.64

0.73

0.75

0.76

8 CQ●CC-COO-CC→C=CC-COO-CC + HO2

2

p, γ

s, β

4.36E+09

0.96

29.81

20.95

37.06

0.53

0.54

0.55

9a CCQ●CC-COO-C→CC=CC-COO-C + HO2 (cis )

2

s, γ

s, β

4.16E+10

0.67

30.94

24.56

40.11

0.31

0.37

0.40

9b CCQ●CC-COO-C→CC=CC-COO-C + HO2 (trans )

2

s, γ

s, β

1.21E+11

0.59

30.07

23.46

40.12

1.12

1.10

1.06

10a CCQ●CC-COO-CC→CC=CC-COO-CC + HO2 (cis )

2

s, γ

s, β

1.71E+11

0.52

31.38

24.73

40.71

0.33

0.41

0.46

10b CCQ●CC-COO-CC→CC=CC-COO-CC + HO2 (trans )

2

s, γ

s, β

5.46E+11

0.43

30.48

23.55

40.17

1.29

1.32

1.29

11 CQ●C(C)C-COO-C→C=C(C)C-COO-C + HO2

1

p, γ

t, β

5.70E+08

1.09

29.41

18.52

37.07

0.45

0.44

0.43

12 CQ●C(C)C-COO-CC→C=C(C)C-COO-CC + HO2

1

p, γ

t, β

7.50E+08

1.07

29.41

18.25

36.12

0.51

0.50

0.49




Page 32 of 45

=

= vii) Class Cγ : the C=C bond of the product olefin at Cγ

Similar to the

Cα= and C=β classes, the formation of the double bond on

Cγ also involves

concerted HO2 eliminations from Cγ /δ sites to peroxy radical at Cδ /γ sites via a planar fivemembered-ring transition state, whose notations are

OOγs −Hδp and OOδp −Hγs , respectively (cf.,

Scheme 6). In this study, the Cγ site is the farthest considered position from the ester group. As expected, the rate constants of the reactions belonging to this class are less influenced by the ester group than those in the

Cα= and C=β classes. Table 7 shows that the ratios of the rate-rule

derived rate constants to the explicitly calculated TST rate constant are approximately two at the given temperatures. Similar to the reactions in the other classes, the change between the methyl and ethyl groups does not noticeably alter the rate constants of the reactions at this site.

= Scheme 6. Reaction scheme for class Cγ , leading to an alkyl-ester olefin whose double bond is

at C γ . The reaction types were given in parentheses.


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Table 7. Fitting Modified Arrhenius Parameters on a per H-atom Basis, Enthalpies, and Entropies of Reactions Used to Derive =

= Rate Rules for the Class Cγ .

No.



Cγ=

1


298

∆rxnH -1

[s ]

[kcal mol ]

7.89E+07

1.37

29.28

k TST/k rate rule

Thermochemistry

AH

-1

∆rxnS

298

-1

-1


600 K

800 K

1000 K

(1.08)

(1.07)

(1.08)

1

CQ●CCC-COO-C→C=CCC-COO-C + HO2

2

p, δ

s, γ

5.83E+07

1.45

28.30

19.40

37.59

1.42

1.18

1.07

2

CQ●CCC-COO-CC→C=CCC-COO-CC + HO2

2

p, δ

s, γ

5.55E+07

1.43

28.40

19.50

37.46

1.05

0.88

0.80

3

CCQ●CC-COO-C→C=CCC-COO-C + HO2

3

s, γ

p, δ

1.18E+08

1.46

29.99

25.17

40.79

0.50

0.59

0.66

3

s, γ

p, δ

3.67E+09

1.14

30.42

25.62

42.81

1.36

1.62

1.78

4

CCQ●CC-COO-CC→C=CCC-COO-CC + HO2




Page 34 of 45

In an attempt to have an overall picture of the reaction rate constants at different sites, the derived rate rules, together with those at the analogous alkyl systems, were plotted in

Figure 6. In addition to being faster, the reactions in class temperature following the increasing order of

Cα= are the least sensitive to

Cα= , C=β , Cγ= and C=x . In other words, the Cα=

reactions play the most important role in the low-temperature regime. Thus, this channel is expected to play a significant role in the formation of the unreactive HO2 radical and unsaturated ester with the double bond at the Cα site. For example, the rate constants at Cα are significantly faster than those at

Cβ ,

C γ and

C x , following the trend of

k α − low > k α -high > k β > k γ > k x . These results are consistent with the calculated values by

Zhang et al.13 and Wang et al.11 for H-abstraction by H atom from methyl and ethyl esters. ǂ

This can be explained by the increasing trend of the reaction barrier (∆V ) at different sites as follows α < β < γ < x . In consequences, it is found that the rate rule classification not only depends on the substituted groups but also depends on the reaction sites to the –COO– ester group (e.g., α , β , γ and x). It is believed that the ester group reduces the energy of both C−OO and C−H bond dissociation in the TS ring on the alkyl chains or/and increases both the energy in the reactions at methyl/ethyl groups. This was explained in terms of hyperconjugation effects as discussed for some ester systems7-8. For the reactions at the alkyl R chain, the strong influence of the ester group (–COO–) is observed at reaction sites close to the ester group (e.g., classes

Cα= −low , Cα=−high and C=β )

due to the nature of breaking C−H and C−OO bond. It is observed in Figure 6 that the rate =

=

= = = constants of class Cγ are slower than those of both classes Cβ and Cα , and the deviation

increases with the temperature decrease. In comparison between the esters and alkanes, the


Page 35 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


=

= rate constants of the concerted HO2 eliminations on Cγ rate rule of esters are quite similar to

those of the alkyl peroxy radicals over the wide temperature range (see Figure 6). The rate constant analysis herein also indicates that the ester group has no considerable impact on the rate constants of concerted HO2 eliminations on the C γ and farther sites (e.g., C δ ) which are not considered in this studied. Regarding the R’ chain (c.f. Figure 3, CH3/C2H5 groups), the hyperconjugation effect of ester group on the energy of C–H and C–OO bond on the C x the relatively low rate constant for the

y

sites11, 52 was observed by

C=x class in 600 - 1000 K in Figure 6. Generally, the

rate rule trend for the concerted HO2 eliminations of the peroxy radicals is k α − low > k α − high > k β > k alkyl − high > k γ > k alkyl > k x . ( k alkyl and k alkyl − high are the rate constants for

the analogous reactions on the alkyl systems to form lowly-substituted and highly-substituted olefins, respectively)18.



Figure 6: Arrhenius plots of the rate rules for the concerted HO2 elimination. [*] Literature data were suggested by Villano et al.18 “alkyl” and “alkyl-high” were referred to form the rate rule of lowly-substituted and highly-substituted olefins, respectively. See Table 2 for the reaction type notation. Several reaction parameters, namely, the reaction enthalpies (∆Erxn), activation energy (∆Vǂ), enthalpies of formation at 298 K (∆Hrxn298 K), the activation energy at 298 K (Ea298 K) and Gibb energy at 298 K (∆rxnG298 K and ∆ǂG298 K), were presented in supporting Table S3. It is observed that the correlation/variation of those parameters is not clear, thus no rules were proposed. Note that the nonnormative variation was found in the classification of concerted elimination in the alkyl + O2 systems18, which do not exhibit the hyperconjugation effect as discussed previously.


Page 36 of 45

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Comparison with non-biodiesel systems It can be observed in Figure 7a that the calculated rate constants at different sites are in good agreement with the previously computed data for methyl propanoate peroxy radicals8 (see Figure 7a) and methyl butanoate peroxy radicals9 (see Figure 7b and 7c). In general, there is good agreement between our calculated values at CBS-QB3 and those suggested by Tao and Lin 9 at G3MP2B3 method. Thus, it is believed that our predictive rate rules, which were systematically derived from the composite CBS-QB3 level, could be confidently used for extrapolating to larger alkyl-ester peroxy radicals.



Figure 7: Comparison of the rate-rule values for selected reactions with literature data: (a)

Cα=−low(cis) , (b) Cα= −low(trans) and (c) C=β classes. Literature values were proposed by [+] Le et al.8 and [‡] Tao and Lin9. See Table 2 for the reaction type notation.


Page 38 of 45

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As demonstrated in our previous study8, the model might be compromised if the rate rules of alkyl + O2 systems are used to estimate the auto-ignition chemistry of esters due to the noticeable influence of the ester groups (–COO–) on the low-temperature kinetics of biodiesel surrogates. Since such an effect is much less important at the C γ site, we compared its rate constant with the previously reported rate constants for the non-ester reactions18, 24, 30, 56

for the considered temperature range of 300 - 2000 K. It is found that the derived rate rule =

= of class Cγ slightly deviates from those of alkyl fuels (e.g., within 1-1.3 times in the

considered temperature range, cf. Figure 8).

=

Figure 8. Comparison of the Cγ rate-rule values with literature data of the alkyl systems. Rate constants were proposed by [*] Villano et al.18 for the lowly-substituted alkyl rate rule, [+] Cartensen et al.30,

[‡]

Huynh et al.24, and

[⁑]

Miyoshi et al.56 for the rate rule type OO p -H p ,

OO p -Hs and OOs -H p . See Table 2 for the reaction type notation.

In summary, due to the noticeable interaction between the reaction sites, the rate rule data for the alkyl systems cannot be used for biological systems, especially for the three



classes

Cα= , C=β and C=x in which the reaction sites are close to the ester group. In other

words, the explicitly derived rate rules in this work must be used for the three classes to correctly construct the detailed kinetic mechanism for biodiesel fuels. CONCLUSIONS Rate estimation rules for the concerted HO2 elimination channel of alkyl methyl/ethyl ester peroxy radicals ( R -C O O -R ' ) were derived from the rate constants calculated from the composite method CBS-QB3 and conventional transition state theory (TST) with corrections from Eckart tunneling and explicit HIR treatments. The calculated thermodynamic and kinetic data are in good agreement with the scattered data in the literature. Based on the quantitative structure-activity relationship, the kinetic behaviors of the title systems were proposed as follows: (1) The alkyl chains ( R either or R ' ) have an unnoticeable effect on the rate at the other group. (2) The ester group (-COO-) increases and decreases the rate constants at the alkyl chain R and R' , respectively, when compared to the non-ester peroxy systems. Such an

effect decreases with the distance between the ester group and the considered reaction sites. (3) The proposed rate rule trend is

kα −low(trans ) > kα −high(β -α ) > kα −low(cis ) > kα −high(α -β ) > k β > ( kγ ≈ kalkyl ) > k x , (c.f. Table 2 for the detailed description). The rate constant (s-1) expressions at different sites are:


Page 40 of 45

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7

1.50

kα −low(trans ) (T) = 3.68 × 10 × T

×

-12227 e T

kα −high(β -α ) (T) = 1.48 × 109 × T1.02 × e kα −low( cis ) (T) = 5.10 × 106 × T1.64 × e kα −high(α -β ) (T) = 9.06 × 107 × T1.30 × e k β (T) = 1.80 × 109 × T1.06 × e k γ (T) = 7.89 × 107 × T1.37 × e 5

k x (T) = 4.20 × 10 × T

2.08

×

-12979 T -12840 T -13326 T -14867 T -14734 T

-14942 e T

SUPPORTING INFROMATION Tables: (1) Comparison of calculated thermodynamic properties of stable structures are formed from reactions in system with experimental data (NIST= Webbook NIST, webbook.nist.gov). Unit: △fH298 in kcal·mol-1, S298 and Cp in cal.mol−1·K−1. (2) Calculated reaction barrier and reaction energy at the CBS-QB3 level comparing with other methods. (3) Parameters for concerted HO2 elimination reactions of Alkyl-Ester peroxy radical calculated with CBS-QB3 method (Unit: kcal/mol). (4) Geometries, energies (at 0 K) and frequencies for all species calculated at the CBS-QB3 level. (5) The thermodynamic properties of the species in the NASA format. ACKNOWLEDGMENTS Computing resources and financial support provided by the Institute for Computational Science and Technology - HCMC, and International University, VNU-HCM are gratefully acknowledged. XTL would like to thank Department of Science and Technology – HCMC for funding (Grant No. 239/QĐ-KHCNTT) and Tan Hoang Vo (University of Technology, VNU-HCM) for helping with the electronic structure calculations



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56. Miyoshi, A., Systematic Computational Study on the Unimolecular Reactions of Alkylperoxy (RO2), Hydroperoxyalkyl (QOOH), and Hydroperoxyalkylperoxy (O2QOOH) Radicals. J. Phys. Chem. A 2011, 115 (15), 3301-25.

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Low-Temperature Oxidation Kinetics of Biodiesel Molecules: Rate

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