Tercera Ola del teatro cuencano: el nacimiento de una nueva era, la

H atom abstraction takes place at primary (β) and tertiary sites (α) of DIPK which results in the formation of two different fuel radicals, denoted as RPri and RTert, (Scheme 7-2). The hydrogen atom is abstracted from DIPK by different radicals (Ṙ) including H, OH, HO², CH3 and C2H5.

Scheme 7-2- DIPK radicals- tertiary and primary radicals

Due to the variation of the activation energy required to dissociate the abstracted H bond, the abstraction reaction is very selective; therefore, the corresponding reaction rate depends on the site from which the H atom is abstracted as well as the radical which abstracts the H atom. The literatures [117] and [118] show that there is numerical agreement between the reactivity of primary β hydrogen of alkanes and that of ketones which is far from the carbonyl group. Therefore the rates of abstraction from β site by H, CH³ and C2H5, (namely (R 9), (R 15) and (R 17)

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respectively), are considered to be analogous to twice of the corresponding rates of abstraction from previously studied ketone, 3-pentanone for which the rates are assigned based on the comparable values in alkanes [119]. The reaction rate for abstraction by HO₂ from DIPK primary β hydrogen, (R 11), is obtained twice of isopropyl methyl ketone (iPMK) based on ab-initio and chemical kinetic study of abstraction reactions by Mendes et. al [120]. The schematic structure of iPMK is shown in Scheme 7-3.

Scheme 7-3- Isopropyl methyl ketone iPMK

Assigning a rate to the H-abstraction reaction from the tertiary α site, however, is more complicated. The α position is next to the carbonyl group which is polar due to the greater electronegativity of oxygen and therefore has larger molecular dipole moments than do alkenes.

The α-hydrogen atom is acidic and can be removed by common bases. The α-substitution reaction in a ketone stands for the substitution of a α-hydrogen atom by an electrophile, E, through either an enol or enolate ion. Since the rates in this study are related to high temperature limit, the details about the abstraction rate at low and intermediate temperature region are not discussed here.

Having obtained the rates of abstraction from β site, the rates of abstraction from α site by H and CH3 are calculated based on the tertiary to primary branching ratio predicted for DIPK H-abstraction by Allen et al [6]. In the absence of branching ratio for C2H5, the abstraction rate from the α site by this radical is updated based on the tertiary to primary branching ratio for a branched alkane, namely isobutene [117]. The reaction rate for abstraction by HO₂ from DIPK tertiary site

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is similarly obtained to be twice of iPMK abstraction rate with HO2 from the tertiary site, based on Mendes et. al [120].

One of the most important oxidation path of ketones are those reactions with OH radical [121]; however, there are few studies on the oxidation behavior of ketones, specifically larger ones.

In a recently published work, the rate constants of OH reaction with large branched and straight chained ketones at combustion temperatures are measured. The OH reaction rate constants for four hexanone isomers were compared. In this study Badra et al [122] showed that the carbonyl group position in the hexanone isomers has negligible effect on the rate constants. In the current study, it is tried to use this concept to estimate the rate constants for DIPK+OH→products, along with Cohen’s [79, 123] method of next-nearest-neighbor (NNN) to specify the site specific rate for primary and tertiary abstracted H. For this purpose, as our first approach, according to Badra et al [122] conclusion for hexanone isomers, it is assumed that the overall reaction rate of OH with isopropyl methyl ketone (iPMK) is approximately the same as its isomer, 3-pentanone. Now

DIPK, iPMK and 3-pentanone are defined using NNN method.

CO

CO T

P

k_DIPK+OH =12 _2, +2 _100, (7-1)

CO CO

CO P T

P

k_iPMK+OH = _1, +6 _2, + _100, (7-2)

S CO

P

k_{3-pentanone+OH} =6 ₁+4 _10, (7-3)

Where P_1,CO is the rate constant for the primary site H abstraction by OH next to the carbonyl C=O, the same as in acetone; P_2,CO and T_100,CO refers to are the rates for primary and tertiary H abstraction by OH from CH and methyl next to the carbonyl group, correspondingly;

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S_10,CO is the rate constant for secondary H-abstraction by OH from CH2 nearby the carbonyl group and P₁ is the rate constant for primary H-abstraction by OH from the methyl group at the site neighboring the CH2 group based on Badra et al [122] definitions. Therefore, DIPK rate will be calculated as follows; Badra et al. [122] estimated 3-pentanone+OH rate based on their calculation of S_10,CO and

P_1,CO and verified their result by Lam et al [124] experimental data. DIPK rate constant with OH can be estimated by analogy approach, (2^nd approach) which is based on using the ab initio calculation of iPMK+OH→productscalculated in terms of overall and site specific rates by Zhou et al [118]. The total rate constants estimated for DIPKreaction with OH at high temperature range (700-2000 K) are illustrated in Figure 7-1 for two approaches which are based on Badra et al rate estimation for 3-pentanone versus Zhou e al [118] rate estimation for iPMK. As it is shown, the rate for the temperatures of over 1000 K are very close for both approaches, however, the rate based on the first approach tends to predict lower reactivity than the second one for 700-1000K.

The rate constants for H abstraction reaction by different radicals are summarized in Table 7-1.

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Figure 7-1- The total rate constants estimated for DIPK reaction with OH at high temperature range

Table 7-1- DIPK estimated rates for H abstraction reactions by H, OH, HO2, CH3 and C2H5 radicals

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