Kinetics of Nonbranched-Chain Processes of the Free-Radical

Home , Kinetic chain length

Global Journal of Science Frontier Research Chemistry Volume 13 Issue 6 Version 1.0 Year 2013 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: 2249-4626 & Print ISSN: 0975-5896

Kinetics of Nonbranched-Chain Processes of the Free-Radical Addition with Reactions, in Which the 1:1 Adduct Radicals Compete for Interaction with Saturated and Unsaturated Components of the Binary Reaction System By Michael M. Silaev Lomonosov Moscow State University, Russia Abstract - Five reaction schemes are suggested for the initiated nonbranched-chain addition of free radicals to the multiple bonds of the unsaturated compounds. The proposed schemes include the reaction competing with chain propagation reactions through a reactive free radical. The chain evolution stage in these schemes involves three or four types of free radicals. One of them is relatively low-reactive and inhibits the chain process by shortening of the kinetic chain length. Based on the suggested schemes, nine rate equations (containing one to three parameters to be determined directly) are deduced using quasi-steady-state treatment. These equations provide good fits for the nonmonotonic (peaking) dependences of the formation rates of the molecular products (1:1 adducts) on the concentration of the unsaturated component in binary systems consisting of a saturated component (hydrocarbon, alcohol, etc.) and an unsaturated component (olefin, allyl alcohol, formaldehyde, or dioxygen). Keywords : low-reactive radical, autoinhibitor, competetion, energy, hydrogen.

GJSFR-B Classification : FOR Code: 030601p

Kinetics ofNonbranched-Chain Processes oftheFree-Radical Addition withReactions, in Which the11 Adduct Radicals Compete for Interaction withSaturated andUnsaturated Components oftheBinary Reaction System

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Kinetics of Nonbranched-Chain Processes of the Free-Radical Addition with Reactions, in which the 1:1 Adduct Radicals Compete for Interaction with Saturated and Unsaturated

Components of the Binary Reaction System 0

2 r

Michael M. Silaev ea Y

Abstract - Five reaction schemes are suggested for the Under other conditions and at other relative reactivities 23 initiated nonbranched-chain addition of free radicals to the of the components, the concentration of the saturated multip le bonds of the unsaturat ed compounds. The proposed component can exceed the concentration of the schemes include the reaction competing with chain unsaturated component so greatly that the most likely propagation reactions through a reactive free radical. The

reaction for the primary adduct radical will be the V chain evolution stage in these schemes involves three or four abstraction of the least strongly bonded atom from a types of free radicals. One of them is relatively low-reactive VI and inhibits the chain process by shortening of the kinetic saturated molecule rather than addition. This reaction ue ersion I

will yield a 1:1 adduct molecule as the ultimate product s

chain length. Based on the suggested schemes, nine rate s equations (containing one to three parameters to be (it proceeds via a nonbranched-chain mechanism since I determined directly) are deduced using quasi-steady-state it regenerates the saturated free radical carrying the treatment. These equations provide good fits for the chain). This reaction may compete with the parallel nonmonotonic (peaking) dependences of the formation rates reaction between the 1:1 adduct radical and an of the molecular products (1:1 adducts) on the concentration unsaturated molecule. Even at a low concentration of of the unsaturated component in binary systems consisting of the unsaturated component, this parallel reaction can a saturated component (hydrocarbon, alcohol, etc.) and an )

proceed more efficiently owing to the formation, from the unsaturated component (olefin, allyl alcohol, formaldehyde, or ( dioxygen). The unsaturated compound in these systems is unsaturated molecule, of a free radical stabilized by the both a reactant and an autoinhibitor generating low-reactive delocalization of the unpaired p-electron over, e.g., a free radicals. A similar kinetic description is applicable to the system of conjugate bonds. This comparatively

nonbranched-chain process of the free-radical hydrogen nonreactive radical does not participate in further chain Research Volume XIII oxidation, in which the oxygen with the increase of its propagation and inhibits the chain process, being concentration begins to act as an oxidation autoingibitor (or an consumed through reactions with the same radical and antioxidant). The energetics of the key radical-molecule with the saturated addend radical. If the adduct radical reactions is considered. Frontier abstracts some labile atom from an unsaturated Keywords : low-reactive radical, autoinhibitor, compete- molecule, it will again turn into the 1:1 adduct molecule, tion, energy, hydrogen. this time via a nonchain mechanism. The 1:1 adduct Science I. Introduction radical (which is the heaviest and the largest among the free radicals that result from the addition of one addend of n a binary system consisting of a saturated radical to the double bond of the molecule) may have an component and an unsaturated one, the abstraction increased energy owing to the energy liberated in the Iof the most labile atom from a saturated molecule by transformation of a C=O, C=C, or O=O double bond Journal some initiator converts this molecule into a saturated into an ordinary bond (30–130 kJ mol–1 for the gas free radical (addend) capable of adding to the double phase under standard conditions [1–4]). Therefore, it bond of an unsaturated molecule to yield a saturated can decompose or react with one of the surrounding Global 1:1 adduct radical. At a sufficiently high concentration of molecules in the place of its formation without diffusing the unsaturated component in the system, this primary in the solution and, hence, without participating in adduct radical can add to another unsaturated molecule radical-radical chain termination reactions. Which of the under certain conditions to yield a secondary, 1:2 two reactions of the adduct radical, the reaction with the adduct radical, and so on, resulting in telomerization. saturated component or the reaction with the unsaturated component, dominates the kinetics of the Author : Department of Chemistry, Lomonosov Moscow State University, Vorob'evy Gory, Moscow 119991, Russia. process will depend on the reactivity and concentration E-mail : [email protected] ratios of the components in the binary system. In the

processes of this kind, in which an addend radical and a case of an overwhelming excess of the saturated low-reactivity, inhibiting radical are involved in three component over the unsaturated component [8,9,12]. types of quadratic-law chain termination reactions, the Based on the reaction schemes suggested for formation rate of the 1:1 adduct as a function of the the kinetic description of the addition process, we have concentration of the unsaturated component has a derived kinetic equations with one to three parameters maximum (which usually occurs at a low concentration to be determined directly. Reducing the number of of this component). unknown parameters in a kinetic equation will allow one Earlier [5,6], there were attempts to describe to decrease the narrowness of the correlation of these such peaking dependences fragmentarily, assuming parameters and to avoid a sharp buildup of the that the saturated or unsaturated component is in statistical error in the nonlinear estimation of these excess, in terms of the direct and inverse parameters in the case of a limited number of

13 proportionalities, respectively, that result from the experimental data points [15]. The rate constant of the 20 simplification of a particular case of the kinetic equation addition of a free radical to the double bond of the set up by the quasi-steadystate treatment of binary unsaturated molecule, estimated as a kinetic parameter, ear

Y copolymerization involving fairly long chains [5]. This can be compared to its reference value if the latter is specific equation is based on an irrational function, known. This provides a clear criterion to validate the 24 whose plot is a monotonic curve representing the mathematical description against experimental data. dependence of the product formation rate on the The kinetic equations were set up using the quasi- concentration of the unsaturated component. This curve steady-state treatment. This method is the most suitable comes out of the origin of coordinates, is convex for processes that include eight to ten or more reactions

V upward, and has an asymptote parallel to the abscissa and four to six different free radicals and are described

VI axis. Replacing the component concentrations with the by curves based on no more than three to seven corresponding mole fractions generates a peak in this experimental points. In order to reduce the exponent of 2 irrational function and thereby makes it suitable to the 2k5[ R1 ] term in the d[ R 2 ]/dt = 0 equation to unity describe the experimental data [7]. However, this [8], we used the following condition for the early stages

circumstance cannot serve as a sufficient validation of the process: k6 = 2k 5 2k7 [1 6] and, hence, V1 = V5

criterion for the mechanism examined, because the new • • 2 • + 2V6 + V7 =( 2k5[ R 1 ]+ 2k7[ R 2 ]) . Here, [R 1 ] and property imparted to the function by the above artificial • transformation does not follow from the solution of the [R 2 ] are the concentrations of the addend radical and the low-reactive (inhibitor) radical, respectively; V1 is the

) set of algebraic equations that are set up for the reaction initiation rate; V , 2V , and V are the rates of the three scheme accepted for the process in a closed system 5 6 7 ( and express the equality of the steady-state formation types of diffusion-controlled quadratic-law chain termination reactions; 2k and 2k are the rate constants and disappearance rates of the reactive intermediates. 5 7 This publication presents a comprehensive of the loss of identical free radicals via the reactions R• + R• and R• + R• , respectively; k is the rate Research Volume XIII Issue ersion I review of the nonbranched-chain kinetic models 1 1 2 2 6 constant of the loss of different free radicals via the developed for particular types of additions of saturated • • free radicals to multiple bonds [8–14]. It covers free R 1 + R 2 reaction (see Schemes 1–5). The kinetic equations thus obtained fit the peaking rate curves well

Frontier radical additions to olefins [10,11], their derivatives [8,9], formaldehyde (first compound in the aldehyde throughout the range of unsaturated component homological series) [8,9,12], and oxygen [13,14] (which concentrations in the binary systems. Our mathematical can add an unsaturated radical as well) yielding various simulation was based on experimental data obtained for Science 1:1 molecular adducts, whose formation rates as a γ-radiation-induced addition reactions for which the of function of the unsaturated compound concentration initiation rate V1 is known.

pass through a maximum (free radical chain additions to a) Addition to Olefins and Their Derivatives the C=N bond have not been studied adequately). In When reacting with olefins not inclined to free-

Journal the kinetic description of these nontelomerization chain radical polymerization, the free radicals originating from

processes, the reaction between the 1:1 adduct radical inefficient saturated telogens, such as alcohols [17] and and the unsaturated molecule, which is in competition amines [18], usually add to the least substituted carbon Global with chain propagation through a reactive free radical atom at the double bond, primarily yielding a free 1:1 • • ( PCl2, C2H5 C HOH, etc.), is included for the first time in adduct radical. This radical accumulates an energy of the chain propagation stage. This reaction yields a low- 90-130 kJ mol–1, which is released upon the • • reactive radical (such as CH2=C(CH3) C H2 or H C =O) transformation of the C=C bond to an ordinary bond and thus leads to chain termination because this radical (according to the data reported for the addition of

does not continue the chain and thereby inhibits the nonbranched C –C alkyl radicals to propene and of 1 4 chain process [8]. We will consider kinetic variants for similar C1 and C2 radicals to 1-butene in the gas phase the case of comparable component concentrations with under standard conditions [1-4]). Such adduct radicals,

an excess of the saturated component [10,11] and the which do not decompose readily for structural reasons,

© 2013 Global Journals Inc. (US) Kinetics of Nonbranched-Chain Processes of the Free-Radical Addition with Reactions, in Which the 1:1 Adduct Radicals Compete for Interaction with Saturated and Unsaturated Components of the Binary Reaction System can abstract the most labile atom from a neighbor The initiation reaction 1 is either the molecule of the saturated or unsaturated component of decomposition of a chemical initiator [5,17,18] or a the binary reaction system, thus turning into a 1:1 reaction induced by light [5,17,18] or ionizing radiation adduct molecule. The consecutive and parallel reactions [19–23]. The overall rate of chain initiation (reactions 1, involved in this free-radical nonbranched-chain addition 1a, and 1b) is determined by the rate of the ratelimiting process are presented below (Scheme 1). In the case of step (k1b > k1a). The reaction between the free radical • comparable component concentrations with a R 2 , which results from reactions 1b and 4, and the nonoverwhelming excess of the saturated component, saturated molecule R1A is energetically unfavorable • extra reaction (1b) (k1b 0) is included in the initiation because it implies the formation of the free radical R 1 , stage [10,11]. In the case of an overwhelming excess of which is less stable than the initial one. The addition the saturated component≠ reaction (1b) is ignored reaction 2 may be accompanied by the abstraction

(k = 0) [8,9,12]. • k • 13

1b 0 2a reaction 2a. R 1 + R2B R1B + R 2 which yields ¾® 2 i. Comparable Component Concentrations the product R1B via a nonchain mechanism. Reaction 2a r • Scheme 1 does not regenerate the addend radical R 1 and is not ea necessary for a kinetic description of the process, Y Chain initiation because the rate ratio of reactions 2 and 2a, V2/V2a = 25 2k1 · 1. I ¾¾®¾ R2 ; k2/k2a, is independent of the concentration of the 0 unsaturated component R2B in the system. The · k · 1a. RR А ¾+ ¾ 1 a ® R А + R ; inhibition of the nonbranched-chain addition process is 0 1 0 1 • due to reaction 4, in which the adduct radical R 3 is · k · V 1b. RR А ¾+ ¾ ® b1 R А + R . spent in an inefficient way, since this reaction, unlike

0 2 0 2 • VI reaction 3, does not regenerate R 1 . The inhibiting effect Chain propagation • is also due to the loss of chain carriers R 1 through their ue ersion I s

• s · k · collisions with lowreactive unsaturated radicals R 2 , but

I 2. RR В ¾+ ¾ 2® R 1 2 3 ; to a much lesser extent. –3 –1 · k3 · The rates of the formation (V, mol dm s ) of 3. RR A ¾+ ¾ ® R + RA . 3 1 3 1 the 1:1 adducts R3A (via a chain mechanism) and R3B Inhibition (via a nonchain mechanism) in reactions 3 and 4 are given by the equations · k4 · В ¾+ ¾ ® В + ) 4. 3RR 2 R3 R 2 .

[g l /( g l + x ) ] a l kV x 21 ( Chain termination V ( AR ) = , (1) 33 2 2k k + a lx + x )( 2 k V · 5 2 15 5. 2R ¾ ¾®¾ Prod ; 1 2 Research Volume XIII ·· k6 [g /( g + xll ) ] V k x 6. RR ¾+ ¾ ® Prod ; = 21 (2) 1 2 V ( 34 BR ) , xk 2 a lx ++ x )( 2 k V · 2k 2 15

7 Frontier 7. R2 ¾ ¾®¾ Prod . 2 where V1 is the rate of the initiation reaction 1; l = [R1A] In this scheme, I is an initiator (e.g., a peroxide and x = [R2B] are the molar concentrations of the initial • [5,12,13]); R 0 is a reactive (initiating) radical; A and B components, with l > x; k2 is the rate constant of the Science • • • are hydrogen or halogen atoms [2,5,17–24]; R 1 is PCl2 addition of the R 1 radical from the saturated component of [19], •CCl [20], alkyl [2,5], 1-hydroxyalkyl [5,6,17,22– 3 R1A to the unsaturated molecule R2B (reaction 2); and

24], or a similar functionalized reactive addend radical g = k1a/k1b and α = k3/k4 are the rate constant ratios for • [5]; R 2 is an alkenyl radical (allyl or higher) [2,5,17–22], competing (parallel) reactions (α is the first chain- Journal 1-hydroxyalkenyl [5,17,18,23,24], or a similar function- transfer constant for the freeradical telomerization • nalized lowreactive (inhibitor) radical [5,18]; R 3 is a process [5]). The rate ratio for the competing reactions

saturated reactive 1:1 adduct radical; R A, R B, and R A Global 0 0 1 is V3/V4 = αl/x, and the chain length is v = V3/V1. are saturated molecules; R2B is an unsaturated Earlier mathematical simulation [8] demon- molecule (olefin or its derivative); R3A and R3B are 1:1 strated that replacing the adduct radical R3 with the adduct molecules; Prod designates the molecular radical R2 [5] in the reaction between identical radicals products resulting from the dimerization or dispro- and in the reaction involving R1 gives rise to a peak in portionation of free radicals. The chain evolution the curve of the 1:1 adduct formation rate as a function

(propagation and inhibition) stage of Scheme 1 include of the concentration of the unsaturated component. consecutive reactions 2 and 3, parallel (competing) Reaction 1b, which is in competition with reaction 1a, is reaction pairs 3 and 4, and consecutiveparallel reaction responsible for the maximum in the curve described by pair 2-4. Eq. (2), and reaction 4, which is in competition with

reaction (3), is responsible for the maximum in the curve 1al xV = , (3a) defined by Eq. (1). 2 2 The number of unknown kinetic parameters to + a lx + x )( x al mm be determined directly (k , , and g ) can be reduced by 2 α where l and x are the component concentrations l and g m m introducing the condition @ α , which is suggested by at the points of maximum of the function. Provided that x the chemical analogy between the competing reactions V is known, the only parameter in Eq. (3a) to be pairs 1a–1b and 3–4. For example, the ratios of the rate 1 determined directly is α. If V is known only for the • • • • 1 constants of the reactions of OH, CH3O , CH3, NO 3 , saturated component R A, then, for the binary system • 1 and H2PO 4 with methanol to the rate constants of the containing comparable R A and R B concentrations, it is 1 2 reactions of the same radicals with ethanol in aqueous better to use the quantity λV , where λ = /( + ) is the 1 l l x solution at room temperature are 0.4–0.5 [25,26]. For mole fraction of R A, in place of V in Eqs. (3) and (3a). 13 the same purpose, the rate constant of reaction 2 in the 1 1

20 The two variable concentrations in the kinetic kinetic equation can be replaced with its analytical equation (3) – l and x – can be reduced to one variable expression k = 2k V / 2 , which is obtained by ear 2 alm 5 1 xm by replacing them with the corresponding mole Y solving the quadratic equation following from the fractions. Substituting the expression k ={ [(1/ ) 2 a χm reaction rate extremum condition ∂V3,4 (1:1 Adduct ) -1]2 -1} 2k V /( + ) ,derived from the rate extremum 26 5 1 lm xm /∂x = 0 , where V3, 4 (1:1 Adduct) = V3 + V4. After these condition, into this transformed equation for the binary

transformations, the overall formation rate equation for system containing comparable component concen-

the 1:1 adducts R3A and R3B (which may be identical, as trations, we obtain

in the case of R3H [5,8,9,12,13,18-21]), appears as V al kV x VI 21 V ,3 4 Adduct)1:1( = = (3) xk 2 a lx ++ x )( 2 k V 2 15

V a ( - )1 χχ = 1 V3, 4 Adduct)1:1( , (3b) χ 2 a -+ + χχ { a χ 2 -- } [ ( 1 ) [ (] 1 / m ) 1 1]

where 1 – χ = l/(l + x) and χ = x/(l + x) are the mole

) fractions of the components R A and R B (0 < <1), 1 2 χ ( respectively, and χm is the χ value at the point of maximum. The overall formation rate of the 1:1 adducts R3A and R3B is a sophisticated function of the formation Research Volume XIII Issue ersion I • • and disappearance rates of the radicals R 1 and R 2 : V (R3A, R3B ) = (V1a +V3 -V5) - (V1b +V4 -V7). The application of the above rate equations to

Frontier particular single nonbranched-chain additions is illustrated in Fig. 1. Curve 1 represents the results of

simulation in terms of Eq. (3b) for the observed 1:1 Science adduct formation rate as a function of the mole fraction

of of the unsaturated component in the phosphorus 1 trichloride–methylpropene re action system at 303 K [19]. In this simulation, the 60Co γ-radiation dose rate –1 Journal was set at P = 0.01 Gy s and the initiation yield was Fig. 1 : Reconstruction of the functional dependences taken to be G(•PCl ) = 2.8 particles per 100 eV (1.60 × 2 (curves) of the product formation rates V3 4 (1,s ) on the –17 , 10 J) of the energy absorbed by the solution [19]. The mole fraction of the unsaturated component (χ) from Global product of reaction 3 is Cl2PCH2C(Cl)(CH3)CH3 (two empirical data (symbols) using Eq. (3b) (model –9 –3 –1 isomers), V1 = 4.65 × 10 mol dm s at χ = 0, and optimization with respect to the parameter α) for the 8 3 –1 –1 2k5 = 3.2 × 10 dm mol s . This leads to α = (2.5 ± phosphorus trichloride-methylpropene reaction system 3 0.4) × 10 , and the rate constant of reaction 2 derived at 303 K [19] (standard deviation of S = 2.58 × 10–6) 4 3 –1 –1 Y from this α value is k2 = (1.1 ± 0.2) × 10 dm mol s . and (2, ○) on the concentration of the unsaturated component (x) from empirical data (symbols) using Eq. 1In an earlier work [10], the methylpropene concentration in this (4a) (model optimization with respect to V1, хm, and α) for system was overvalued by a factor of 1.7 when it was derived from the the 2-propanol–2-propen-1-ol system at 433 K [23] –7 mole fractions given in [19] . (SY = 5.91 × 10 ).

Note that, if the R2–B bond dissociation energy a function of the concentration of the unsaturated for the unsaturated component of the binary system is component in the reaction system 2-propanol–2- approximately equal to or above, not below, the R1–A propen-1-ol at 433 K [8,9]. In this description, we used a bon d dissociation energy for the saturated component, 60Co γ-radiation dose rate of P = 4.47 Gy s–1 [23]. The than the rate of reaction 4 relative to the rate of the product of reactions 3 and 4 is CH3 (CH3)C(OH) 10 3 –1 –1 parallel reaction 3 (chain propagation through the CH2CH2CH2OH, and 2k5 = 1.0 × 10 dm mol s . The • reactive free radical R 1 ) will be sufficiently high for f ollowing parameters were obtained: V1 = (3.18 ± 0.4) × 6 –3 –1 –2 –3 adequate description of R3A and R3B adduct formation 10 mol dm s , xm = (3.9 ± 0.5) × 10 mol dm , an d in terms of Eqs. (1)–(3b) only at high temperatures [20]. α = (6.8 ± 0.8) × 10–2. The rate constant of reaction 2 In the phosphorus trichloride–propene system, the derived from this α is k = (1.0 ± 0.14) × 105 dm3 2 difference between the R –B (B = H) and R –A (A = mol–1 s–1. 2 1 Hal) bond dissociation energies in the gas phase under 13 0 b) Addition to Formaldehyde standard conditions [1] is as small as 5 kJ mol–1, while in 2 Free radicals add to the carbon atom at the the tetrachloromethane-methylpropene (or cyclohexene) r double bond of the carbonyl group of dissolved free ea and bromoethane-2-methyl-2-butene systems, this Y (unsolvated, monomer) formaldehyde. The concen- difference is 20.9 (37.7) and ~24 kJ mol–1, respectively. tration of free formaldehyde in the solution at room 27 ii. Excess of the Saturated Component temperature is a fraction of a percent of the total If the concentration of the saturated component formaldehyde concentration, which includes formal- exceeds the concentration of the unsaturated dehyde chemically bound to the solvent [27]. The component in the binary system, reaction 1b can be concentration of free formaldehyde exponentially V neglected. If this is the case (k1b = 0), then, in the increases with increasing temperature [28]. The energy numerators of the rate equations for reactions 3 and 4 released as a result of this addition, when the C=O VI

(Eqs. (1) and (2)), gl /(gl + x) = 1 and the overall rate bond is converted into an ordinary bond, is 30 to 60 kJ ue ersion I s equation for the formation of the 1:1 adducts R A and mol –1 (according to the data on the addition of C –C s 3 1 4 I R3B will appear as = alkyl radicals in the gas phase under standard conditions [1–4]). The resulting free 1:1 adduct radicals

1 a lV + x )( k 2 x can both abstract hydrogen atoms from the nearest- V Addduct1:1( ) = = 3, 4 2 neighbor molecules of the solvent or unsolvated xk a lx ++ x )( 2 k V 2 15 formaldehyde and, due to its structure, decompose by a

) (4) monomolecular mechanism including isomerization

[9,12]. ( 1 xV = (4a) 2 - 2 i. Addition of Free 1-Hydroxyalklyl Radicals with Two x æ α l 1 ö + m + or More Carbon Atoms αl + x ç x ÷ m Research Volume XIII è αlm ø Free 1-hydroxyalkyl radicals (which result from the abstraction of a hydrogen atom from the carbon where the parameters are designated in the same atom bonded to the hydroxyl group in molecules of way as in Eqs. (1)-(3a), l >> x, and k = [( al / x )+ saturated aliphatic alcohols but methanol under the Frontier 2 m m 2 action of chemical initiators [29,30], light [17,31], or (1/ al ) ] 2k V is determined from the condition ∂V , m 5 1 3 4 ionizing radiation [32,33]) add at the double bond of free (1:1Adduct) / ∂х = 0. formaldehyde dissolved in the alcohol, forming 1,2- The rate equations for the chain termination Science alkanediols [8,9,12,29–36], carbonyl compounds, and reactions 5–7 (Scheme , k = 0) are identical to Eqs. of 1 1b methanol [8,33] via the chaining mechanism. (The yields (9)–(11) (see below) with = 0. β of the latter two products in the temperature range of Note that, if it is necessary to supplement 303 to 448 K are one order of magnitude lower.) In these

Scheme 1 for k = 0 with the formation of R B via the Journal 1b 1 processes, the determining role in the reactivity of the possible nonchain reaction 2a (which is considered in alcohols can be played by the desolvation of the Section a), the parameter k should be included in 2a formaldehyde in alcohol–formaldehyde solutions, which the denominator of Eq. (4) to obtain k x2 +(al+x) (k x Global 2 2a depends both on the temperature and on the polarity of + 2k5V1). the solvent [28,33]. For the γ-radiolysis of 1(or 2)-

The analytical expression for k2 in the case of propanol–formaldehyde system at a constant temper- k2a 0 is identical to the expression for k2 for Eq. (4). ature, the dependences of the radiation -chemical yields

The equation for the rate V2a (R1B) can be derived by of 1,2-alkanediols and carbonyl compounds as a replacing ≠ k2 with k2a in the numerator of Eq. (4) function of the formaldehyde concentration show containing k2a in its denominator. maxima and are symbatic [8,32]. For a constant total Curve 2 in Fig. 1 illustrates the good fit between formaldehyde concentration of 1 mol dm–3, the Eq. (4a) and the observed 1:1 adduct formation rate as dependence of the 1,2-alkanediol yields as a function of

temperature for 303–473 K shows a maximum, whereas and 1- and 2-propanol gives ethanediol, carbon the yields of carbonyl compounds and methanol monoxide, and hydrogen in low radiation-chemical increase monotonically [33] (along with the yields (which, however, exceed the yields of the same concentration of free formaldehyde [28]). In addition to products in the γ-radiolysis of individual alcohols) the above products, the nonchain mechanism in the γ- [8,9,33]. The available experimental data can be radiolysis of the solutions of formaldehyde in ethanol described in terms of the following scheme of reactions:

Scheme 2 Chain initiation

2k 1 · 1. I ¾¾® 2R ; 13 0 20 k · ¾a1 ®¾ • 1а . R0 + ROH R0 H + R (–H)OH. ear

Y Chain propagation 28 k • ¾2 ®¾ • 2. R(–H) OH + CH 2O R (–H) (ОH)СН 2О ; k • ¾3 ®¾ • 3. R(–H) (ОH)СН 2О + ROH R (–H)(ОH)СН2ОH + R(–H)O; V k 3 a VI • ¾ ®¾ • 3а. R (–H)(ОH)СН2О R(–2H)HO + СН 2ОН

• (or R¢R ¢¢ CO + СН 2ОН);

• k b3 • 3b. СН2ОН + ROH ¾ ®¾ CH3OH + R(–H) OH.

Inhibition

• k4 • ) ¾®¾ 4. R(–H)(ОH)СН 2О + CH2O R (–H)(ОH)СН 2ОH + СНО. ( Chain termination

2k • ¾¾®¾ 5 5. 2 R(–H) OH R (–H)(OH)R (–H)OH

Research Volume XIII Issue ersion I (or: ROH + R(–2H)HO,

¢R ¢¢ CO);

Frontier ROH + R

k • • ¾6 ®¾ 6. R (–H)OH + СНО R (–H)(OH)CHO

Science (or: ROH + R(–2H)HO + O2, of ROR + O , 3 RO2R + O2); Journal • 2k7 7. 2 СНО ¾¾ ®¾ RO2R + 2О3.

Global (or: CH2O + CO,

2CO + H2).

• • In these reactions, I is an initiator, e.g., a CH2OH, the 1-hydroxymetyl fragment radical; R(–H)OH, • peroxide [29,30]; R 0 , some reactive radical (initiator the reactive 1-hydroxyalkyl radical (adduct radical), radical); R, an alkyl; ROH, a saturated aliphatic alcohol, beginning from 1-hydroxyethyl; •CHO, the low-reactive either primary or secondary, beginning from ethanol; formyl radical (inhibitor); R0H, the molecular product; CH2O, the unsaturated molecule – free formaldehyde; R(–H)(OH)CH2OH, 1,2-alkanediol; R(–2H)HO, an aldehyde

in the case of a primary alcohol and an R'R"CO ketone in competition with reaction 3b, is not included as well,

the case of a secondary alcohol; R(–H)(OH)R(–H)OH, a because there is no chain formation of ethanediol at v icinal alkanediol; R(–H)(OH)CHO, a hydroxyaldehyde. 303–448 K [33]. At the same time, small amounts of The chain evolution stage of Scheme 2 includes ethanediol can form via the dimerization of a small consecutive reaction pairs 2–3, 2–3a, and 3a–3b; fraction of hydroxymethyl radicals, but this cannot have parallel (competing) reaction pairs 3–3a, 3–3b, 3–4, and any appreciable effect on the overall process kinetics. 3a–4; and consecutive–parallel reactions 2 and 4. The addition of free formyl radicals to formaldehyde Scheme 2 does not include the same types of cannot proceed at a significant rate, as is indicated by radical-molecule reactions as were considered in the fact that there is no chain formation of glycol Section a for Scheme 1. In addition, it seems unlikely aldehyde in the systems examined [33]. that free adduct radicals will add to formaldehyde at The mechanism of the decomposition of the

free adduct radical via reaction 3a, which includes the 13 higher temperatures the reaction of adding is unlikely 0 because this would result in an ether bond. The addition formation of an intramolecular H…O bond and 2 of hydroxymethyl radicals to formaldehyde, which is in isomerization, can be represented as follows [8,9,12]: r ea

VI The probability of the occurrence of reaction 3a a higher electron affinity [1]. For example, in contrast to ue ersion I

should increase with increasing temperature. This is the methyl and alkoxyl π-radicals, the formyl σ -radical s

s indicated by experimental data presented above can be stabilized in glassy alcohols at 77 K [37]. In the I [8,9,12]. The decomposition of the hydroxyalkoxyl gas phase, the dissociation energy of the C–H bond in • radical. R(–H)(OH)CH2O (reaction 3a) is likely formyl radicals is half that for acetyl radicals and is endotherm ic. The endothermic nature of reaction 3a is about 5 times lower than the dissociation energy of the indirectly indicated by the fact that the decomposition of Cα–H bond in saturated C1–C3 alcohols [1]. • simple C24- C alkoxyl radicals RO in the gas phase is As distinct from reactions 3 and 3a,b, reaction 4 o )

accompanied by heat absorption: (ΔH 298 = 30-90 kJ leads to an inefficient consumption of hydroxyalkoxyl

mol–1 [2-4]). Reaction 3b, subsequent to reaction 3a, is adduct radicals, without regenerating the initial 1- ( exothermic, and its heat for C2- C3 alcohols in the gas hydroxyalkyl addend radicals. Reaction 4 together with o –1 phase is ΔH 298 = -40 to -60 kJ mol [2–4]. As follows reaction 6 (mutual annihilation of free formyl and chain- from the above scheme of the process, reactions 3a carrier 1-hydroxyalkyl radicals) causes the inhibition of Research Volume XIII and 3b, in which the formation and consumption of the the nonbranched-chain process. For the dispropor- highly reactive free radical hydroxymethyl take place (at tionation of the free radicals, the heats of reactions 5–7 equal rates under steady-state conditions), can be for C1–C3 alcohols in the gas phase vary in the range of

Frontier o –1 represented as a single bimolecular reaction 3a,b ΔH 298 = -135 to -385 kJ mol [1-4]. occurring in a "cage" of solvent molecules. The rates of the chain formation of 1,2-

The free formyl radical resulting from reaction 4, alkanediols in reaction 3 (and their nonchain formation in Science which is in competition with reactions 3 and 3a, is reaction 4), carbonyl compounds in reaction 3a, and comparatively low -reactive because its spin density can methanol in reaction 3b are given by the following of be partially delocalized from the carbon atom via the equations: double bond toward the oxygen atom, which possesses Journal a lV + x )( k x 1 2 V3, 4(R(–H)(OH)CH2OH) = , (5) 2 lxk x (a ++ b + xl ) 2 k V Global 2 15

b kV x 1 2 V3a (R (–2H) HO) = V3b (CH3OH) = , (6) 2 lxk x (a ++ b + xl 2) k V 2 5 1

where V1 is the initiation rate, l is the molar concentration concentration of free formaldehyde (l >> x), k2 is the of the saturated alcohol at a given total concentration of rate constant of reaction 2 (addition of 1-hydroxyalkyl 2 formaldehyde dissolved in it, x is the molar free radical to free formaldehyde), and α = k3/k4 and

–3 β = k3а/k4 (mol dm ) are the ratios of the rate constants

of the competing (parallel) reactions. Estimates of 2k5 were reported by Silaev et al. [39,40]. From the extremum condition for the reaction 3a rate function,

∂V3a /∂х = 0, we derived the following analytical

2 expression: k2 = (alm + β ) 2k 5V1 /x m . The overall process rate is a complicated function of the formation and disappearance rates of the • • R(–H)OH and CHO free radicals: V(R(–H)(OH)CH2OH,

R(–2H)HO, CH3OH) = V1a + V3 + V3b – V4 – V5 + V7. The

13 ratios of the rates of the competing reactions are V3/V4 =

20 αl/x and V3a/V4 = β/x, and the chain length is v = (V3 +

V3a)/V1. The ratio of the rates of formation of 1,2- ear Y alkanediol and the carbonyl compound is a simple linear

function of x: V3, 4 (R(–H)(OH)CH2OH)/V3a(R( –2H)HO) = 30 (k4/k3а)х + ( k3/ k3а)l. Th e equations for the rates of chain- termination reactions 5–7 are identical to Eqs. (9)–(11) (see below).

Figure 2 illustrates the use of Eqs. (5) and (6) for

V describing the experimental dependences of the Fig. 2 : Reconstruction of the functional dependence

VI formation rates of 1,2-butanediol (curve 1) in reactions 3 (curves) of the product formation rates V3, 4 and V3а on

and 4 and propanal (curve 2) in reaction 3a on the the concentration x of free formaldehyde (model

concentration of free formaldehyde in the 1-propanol– optimization with respect to the parameters α, β and k2)

formaldehyde reacting system at a total formaldehyd e from empirical data (symbols) for the 1-propanol–

concentration of 2.0 to 9.5 mol dm–3 and temperature of formaldehyde system at 413 K [8,9,41]: (1,∆) calculation –7 413 K [8,9,41]. The concentration dependence of the using Eq. (5), standard deviation of SY = 2.20 × 10 ; –8 propanal formation rate was described using the (2, □) calculation using Eq. (6), SY = 2.38 × 10 .

estimates of kinetic parameters obtained for the same Note that, as compared to the yields of 1,2 -

) dependence of the 1,2-butanediol formation rate. We propanediol in the γ-radiolysis of the ethanol– considered these data more reliable for the reason that ( formaldehyde system, the yields of 2,3-butanediol in the the carbonyl compounds forming in the alcohol– γ-radiolysis of the ethanol–acetaldehyde system are one formaldehyde systems can react with the alcohol and order of magnitude lower [41]. Using data from [8,9], it this reaction depends considerably on the temperature can be demonstrated that, at 433 K, the double bond of Research Volume XIII Issue ersion I and acidity of the medium [27]. The mathematical 2-propen-1-ol accepts the 1-hydroxyethyl radical 3.4 modeling of the process was carried out using a 137Cs times more efficiently than the double bond of γ-radiation dose rate of P = 0.8 Gy s–1 [32,41], a total • formaldehyde [42].

Frontier initiation yield of G(CH CH C HOH) = 9.0 particles per 3 2 ii. Addition of the Hydroxymethyl Radical 100 eV [8,9] (V = 4. 07 × 10–7 mol dm–3 s–1), and 2k = 1 5 The addition of hydroxymethyl radicals to the 4.7 × 109 dm3 mol–1 s–1). The following values of the carbon atom at the double bond of free formaldehyde Science parameters were obtained: α = 0.36 ± 0.07, β = 0.25 molecules in methanol, initiated by the free -radical ± 0.05 mol dm–3, and k = (6.0 ± 1.4) × 103 dm3 of 2 –1 –1 mechanism, results in the chain formation of ethanediol mol s . [34]. In this case, reaction 3a in Scheme 2 is the reverse • of reaction 2, the 1-hydroxyalkyl radical R(–H)OH is the Journal • hydroxymethyl radical CH2OH, so reaction 3b is eliminated( k3b = 0), and reaction 5 yields an additional amount of ethanediol via the dimerization of chain- Global carrier hydroxymethyl radicals (their disproportionation can practically be ignored [43]). The scheme of these reactions is presented in [35]. The rate equation for ethanediol formation by the chain mechanism in reaction 3 and by the nonchain 2 The alcoh ol concentration in alcohol–formaldehyde solutions at any mechanism in reactions 4 and 5 in the methanol– temperature can be estimated by the method suggested in [38,39]. formaldehyde system has a complicated form3 as The data necessary for estimating the concentration of free

formaldehyde using the total formaldehyde concentration in the compared to Eq. (1) for the formation rate of the other

solution are reported by Silaev et al. [28,39]. 1,2-alkanediols [12]:

22 V3, 4 , 5 (CH2OH) 2 = 1 [ fV a xl )( k ++ 12 5 (2 a b ++ ) ] fxlkVx (7)

2 where f = k x + ( αl + β + x ) 2 Vk . 2 15

If the rate of ethanediol formation by the tetraoxyalkyl, 1:2 adduct radical, which is the heaviest dimerization mechanism in reaction 5 is ignored for the and the largest among the reactants. It is less reactive reason that it is small as compared to the total rate of than the primary, 1:1 peroxyl adduct radical and, as a ethanediol formation in reactions 3 and 4, Eq. (7) will be consequence, does not participate in further chain identical to Eq. (5). After the numerator and denominator propagation. At moderate temperatures, the reaction on the right-hand side of Eq. (5) are divided by k–2 ≡ k3a, proceeds via a nonbranchedchain mechanism. 13 0 one can replace k in this equation with K = k /k , 2 2 2 –2 i. Addition of Hydrocarbon Free Radicals 2 which is the equilibrium constant for the reverse of Usually, the convex curve of the hydrocarbon r reaction 2. Ignoring the reverse of reaction 2 (k3a = 0, ea (RH) autooxidation rate as a function of the partial Y β = 0) makes Eq. (5) identical to Eq. (4) in Scheme 1 pressure of oxygen ascends up to some limit and then (see the Section a). In this case, the rate constant k2 is 31 flattens out [6]. When this is the case, the oxidation effective. kinetics is satisfactorily describable in terms of the c) Addition to Oxygen conventional reaction scheme [2,5,6,16,44,45], which

The addition of a free radical or an atom to one involves two types of free radicals. These are the of the two multiply bonded atoms of the oxygen hydrocarbon radical R• (addend radical) and the V molecule yields a peroxyl free radical and thus initiates • addition product RO (1:1 adduct radical). However, the VI 2 oxidation, which is the basic process of chemical existing mechanisms are inapplicable to the cases in ue ersion I evolution. The peroxyl free radical then abstracts the s which the rate of initiated oxidation as a function of the s

I most labile atom from a molecule of the compound oxygen concentration has a maximum (Figs. 3, 4) being oxidized or decomposes to turn into a molecule of [46,47]. Such dependences can be described in terms an oxidation product. The only reaction that can of the competition kinetics of free-radical chain addition, compete with these two reactions at the chain evolution whose reaction scheme involves not only the above two stage is the addition of the peroxyl radical to the oxygen • types of free radicals, but also the RO 4 radical (1:2 molecule (provided that the oxygen concentration is adduct) inhibiting the chain process [13,14]. ) sufficiently high). This reaction yields a secondary,

( Scheme 3 Chain initiation 2k · ¾ 1®¾ Research Volume XIII 1. I R2 0 ; · k · 1а ¾+ ¾ 1 a ® Н + . 0 R HR R0 .R Frontier Chain propagation

·· · k 2 2. OR 2 ¾+ ¾ ® RO 2 ; Science · k 3 · 3. RО2 RH ¾+ ¾ ® RО2 + RH of • (or ROH + RO);

· k Journal RО ¾ 3а ®¾ ¢ ¢¢ • 3a. 2 R (–H) HO + R O • (or R HO + OH); (–2H) Global • • k b3 • 3b. R¢¢O (RO ) + RH ¾®¾ R¢¢ OH (ROH) + R

• k3b (or OH + RH ¾®¾ H O + R• 2 Inhibition k · 4. RО· O ¾+ ¾4 ® RO . 2 2 4

3In an earlier publication [8], this equation does not take into account reaction 3a.

Chain termination

· 2k 5. 2R ¾®¾ 5 RR

(or R(–2H)H + RH);

k • · ¾6 ®¾ 6. R + RO4 RH + R(–2H)HО + O3

(or: R(–2H)H + R(–2H)HО + H2О + О2,

ROH + R HO + O , 13 (–2H) 2 20 ROR + O3 ,

ear

Y RO2R + O2);

32 · 2k7 7. 2RO ¾®¾ ¾ R H + R HО + H O + 3O or 2O 4 (–2H) (–2H) 2 2 3

(or: ROH + R HO + 3O or 2О , (–2H) 2 3

V 2R(–2H)HO + H2O2 + 2О2, VI

2R(–2Н)НО + Н2О + О3 + О 2,

RO2R + 3О2 or 2О3).

The only difference between the kinetic model (alternative) pathway of reaction 3 consists of four steps, of oxidation represented by Scheme 3 and the kinetic namely, the breaking of old bonds and the formation of model of the chain addition of 1-hydroxyalkyl radicals to two new bonds in the reacting structures. In reaction 3a,

) the free (unsolvated) form of formaldehyde in the isomerization and decomposition of the alkylperoxyl • nonmethanolic alcohol–formaldehyde systems [8,9] radical adduct RO 2 with O–O and C–O or C–H bond ( (Scheme 2, Section b) is that in the former does not breaking take place [6,44], yielding the carbonyl

include the formation of the molecular 1:1 adduct via compound R¢(–H)HO or R(–2H)HO. Reaction 3b produces reaction 4. the alcohol R”OH or water and regenerates the free • Research Volume XIII Issue ersion I The decomposition of the initiator I in reaction 1 radical R (here, R¢ and R¢¢ are radicals having a smaller • yields a reactive R 0 radical, which turns into the ultimate number of carbon atoms than R). As follows from the product R0H via reaction 1a, generating an alkyl radical above scheme of the process, consecutive reactions 3a •

Frontier R , which participates in chain propagation. In reaction and 3b (whose rates are equal within the quasi-steady- 2, the addition of the free radical R• to the oxygen state treatment), in which the highly reactive fragment, molecule yields a reactive alkylperoxyl 1:1 adduct oxyl radical R¢¢O• (or •OH) forms and then disappears, • radical RO 2 [45], which possesses increased energy respectively, can be represented as a single, combined Science owing to the energy released upon the conversion of the bimolecular reaction 3a, b occurring in a "cage" of of O=O bond into the ordinary bond RO–O• (for addition in solvent molecules. Likewise, the alternative the gas phase under standard conditions, this energy is (parenthesized) pathways of reactions 3 and 3b, which –1 • 115–130 kJ mol for C1–C4 alkyl radicals [1,2,4] and 73 involve the alkoxyl radical RO , can formally be treated Journal –1 kJ mol for the allyl radical [4]). Because of this, the as having equal rates. For simple alkyl C1–C4 radicals R, adduct radical can decompose (reaction 3a) or react the pathway of reaction 3 leading to the alkyl o with some neighbor molecule (reaction 3 or 4) on the hydroperoxide RO2H is endothermic (ΔH 298 = 30–80 kJ Global spot, without diffusing in the solution and, accordingly, mol–1) and the alternative pathway yielding the alcohol o –1 without entering into any chain termination reaction. In ROH is exothermic (ΔH 298 = –120 to –190 kJ mol ), reaction 3, the interaction between the radical adduct while the parallel reaction 3a, which yields a carbonyl • • RO 2 and the hydrocarbon molecule RH yields, via a compound and the alkoxyl radical R¢¢O or the hydroxyl • o chain mechanism, the alkyl hydroperoxide RO2H (this radical OH, is exothermic in both cases (ΔH 298 = –80 • –1 o reaction regenerates the chain carrier R and, under to –130 kJ mol ), as also is reaction 3b (ΔH 298 = –10 certain conditions, can be viewed as being reversible to –120 kJ mol–1), consecutive to reaction 3a, according [2]) or the alcohol ROH (this is followed by the to thermochemical data for the gas phase [2–4]. In regeneration of R• via reaction 3b). The latter reaction 4, which is competing with (parallel to)

reactions 3 and 3a (chain propagation through the stabilized by a weak intramolecular H···O hydrogen reactive radical R•), the resulting low-reactive radical that bond [54] shaping it into a six-membered cyclic does not participate in further chain propagation and structure6 (seven-membered cyclic structure in the case inhibits the chain process is supposed to be the of aromatic and certain branched acyclic hydrocarbons) 4,5 • alkyltetraoxyl 1:2 radical adduct RO 4 , which has the [56,57]: largest weight and size. This radical is possibly

13 0

r ea

Y Reaction 4 in the case of the methylperoxyl ethers, and organic peroxides containing fewer carbon radical CH O• adding to the oxygen molecule to yield atoms than the initial hydrocarbon, as in the case of the 33 23 • • alkylperoxyl radical RO2 in reaction 3a. At later stages of the methyltetraoxyl radical CH O43 takes place in the gas phase, with heat absorption equal to 110.0 ± 18.6 kJ oxidation and at sufficiently high temperatures, the mol–1 [2 0] (without the energy of the possible formation of resulting aldehydes can be further oxidized into a hydrogen bond taken into account). The exothermic respective carboxylic acids. They can also react with V • • molecular oxygen so that a C–H bond in the aldehyde reactions 6 and 7, in which the radical R or RO VI 4 molecule breaks to yield two free radicals ( • and undergoes disproportionation, include the isomerization HO2 ue ersion I

• • • s R′(–H)O or R(–2H)O). This process, like possible ozone s and decomposition of the RO4 radical (taking into • • I account the principle of detailed balance for the various decomposition yielding an O atom or peroxide reaction pathways). The latter process is likely decomposition with O–O bond breaking, leads to accompanied by chemiluminescence typical of degenerate chain branching [5]. hydrocarbon oxidation [23]. These reactions regenerate The equations describing the formation rates of 5 molecular products at the chain propagation and oxygen as O2 molecules (including singlet oxygen [23, termination stages of the above reaction scheme, set up ) 30]) and, partially, as O3 molecules and yield the carbonyl

compound R HO (possibly in the triplet excited state using the quasi-steady-state treatment, appear as ( (–2H) [23]). Depending on the decomposition pathway, the follows: other possible products are the alcohol ROH, the ether V3(RO2H; ROH) = al kV fx = (8) ROR, and the alkyl peroxide RO2R. It is likely that the 21 Research Volume XIII isomerization and decomposition of the RO• radical via 4 = a 1 l xV fm , (8a) reactions 6 and 7 can take place through the breaking of a C–C bond to yield carbonyl compounds, alcohols, V 3а(R¢(–H) HO; R(–2H) HO) = V3b(R¢¢ OH; H2O) = Frontier

4It is hypothesized that raising the oxygen concentration in the • o-xylene–oxygen system can lead to the formation of an [RO ··· O2] = b kV x f = (9) • 21 intermediate complex [46] similar to the [ROO ··· (π-bond)RH] Science complex between the alkylperoxyl 1:1 adduct radical and an unsaturated hydrocarbon suggested in this work. The electronic = b xV f (9a) 1 m , of π structure of the -complexes is considered elsewhere [48]. 5 2 Thermochemical data are available for some polyoxyl free radicals 2 2 V5 = V 1 2 k 5 (a b ++ xl ) f , (10) (the enthalpy of formation of the methyltetraoxyl radical without the energy of the possible intramolecular hydrogen bond Н···О taken into Journal • –1 22 account is ΔНf˚298( CH3O4 ) = 121.3 ± 15.3 kJ mol ) and polyoxides –1 2V6 = 2 V 2 k V (a b ++ xl ) k x f , (11) (ΔНf˚298(CH3O4H) = –21.0 ± 9 kJ mol ) [49]. These data were 51 1 2 obtained using the group contribution approach. Some Global 2 2 physicochemical and geometric parameters were calculated for the ( 2 ) V7 = V k 21 x f , (12) methyl hydrotetraoxide molecule as a model compound [50–52]. The IR spectra of dimethyl tetraoxide with isotopically labeled groups in Ar– where V is the initiation rate, = [RH] and = [O ] are O2 matrices were also reported [53]. For reliable determination of the 1 l x 2 number of oxygen atoms in an oxygen-containing species, it is the molar concentrations of the starting components

necessary to use IR and EPR spectroscopy in combination with the (l >> x), α = k /k and β = k /k (mol dm–3) are the isotope tracer method [53]. 3 4 3a 4 ratios of the rate constants of the competing (parallel) 6 The R(–H)H···O(R)O3 ring consisting of the same six atoms (C, H, and 4O), presumably with a hydrogen bond [6], also forms in the transition 7 • state of the dimerization of primary and secondary alkylperoxyl Note that the alkylperoxyl radicals RO 2 are effective quenchers of • 1 radicals RО 2 via the Russell mechanism [5,55]. singlet oxygen O2( a D g ) [58].

2 reactions, k 2 = (alm+ β ) 2k5V 1 / x m is the rate constant last two lead to an oxidation rate versus oxygen of the addition of the alkyl radical R• to the oxygen concentration curve that emanates from the origin of m olecule (reaction 2) as determined by solving the coordinates, is convex upward, and has an asymptote quadratic equation following from the rate function parallel to the abscissa axis. Such monotonic

extremum condition ∂ V3,3a / ∂x = 0, l m and xm are the dependences are observed when the oxygen solubility values of l and x at the maximum point of the function, in the liquid is limited under given experimental 8 2 2 conditions and the oxygen concentration attained is and f = k2x + (αl + β + x) 2k5V1 , and fm = x + 2 [O2]top ≤ xm. (al + β + x) xm (alm + β ). Unlike the conventional model, the above The ratios of the rates of the competing kinetic model of free-radical nonbranchedchain reactions are V /V = αl/x and V /V = β/x, and the chain 3 4 3a 4 oxidation, which includes the pairs of competing length is v = (V3 + V3a)/V1. Eq. (9) is identical to Eq. (6). 13 reactions 3–4 and 3a–4 (Scheme 3), allows us to

20 Eqs (8a) and (9a) were obtained by replacing the rate describe the nonmonotonic (peaking) dependence of constant k in Eqs. (8) and (9) with its analytical 2 the oxidation rate on the oxygen concentration (Fig. 3). ear expression (for reducing the number of unknown Y In this oxidation model, as the oxygen concentration in parameters to be determined directly). the binary system is increased, oxygen begins to act as 34 For αl >> β (V >> V ), when the total yield of 3 3a an oxidation autoinhibitor or an antioxidant via the further alkyl hydroperoxides and alcohols having the same oxidation of the alkylperoxyl 1:1 adduct radical RO• into number of carbon atoms as the initial compound far 2 the low-reactive 1:2 adduct radical RO • (reactions 4 exceeds the yield of carbonyl compounds, as in the 4 and 6 lead to inefficient consumption of the free radicals case of the oxidation of some hydrocarbons, the V RO• and R• and cause shortening of the kinetic chains). parameter β in Eqs. (8) and (8a) can be neglected 2 VI The optimum oxygen concentration x , at which the (β = 0) and these equations become identical to Eqs. m oxidation rate is the highest, can be calculated using (3) and (3a) with the corresponding analytical kinetic equations (8a) and (9a) and Eq. (3a) with = 0 expression for k . β 2 or the corresponding analytical expression for k . In the In the alternative kinetic model of oxidation, 2 familiar monograph Chain Reactions by Semenov [60], it whose chain termination stage involves, in place of R• is noted that raising the oxygen concentration when it is (Scheme 3), RO • radicals reacting with one another and 2 already sufficient usually slows down the oxidation with RO• radicals, the dependences of the chain 4 process by shortening the chains. The existence of the formation rates of the products on the oxygen

) upper (second) ignition limit in oxidation is due to chain concentration derived by the same method have no x termination in the bulk through triple collisions between ( maximum: V3 =V1k3l / (k4 x+ 2k51V1 ) and V3a =V1k3a (k4x+ an active species of the chain reaction and two oxygen molecules (at sufficiently high oxygen partial pressures). 2k5V1). In the kinetic model of oxidation that does not include the competing reaction 4 (k = 0) and involves In the gas phase at atmospheric pressure, the number 4 3 Research Volume XIII Issue ersion I • • • of triple collisions is roughly estimated to be 10 times the radicals R and RO 2 (the latter instead of RO 4 in Scheme 3) in reactions 5–7, the reaction rate functions smaller than the number of binary collisions (and the probability of a reaction taking place depends on the V3 and V3a obtained in the same way are fractional

Frontier specificity of the action of the third particle). rational functions in the form of a0 x/(b0x + c0), where a 0, Curve 1 in Fig. 3 illustrates the fit between Eq. b0, and c0 are coefficients having no extremum. For a similar kinetic model in which reactions 3a,b and 4 (3a) at αl >> β and experimental data for the radiation-

Science induced oxidation of o-xylene in the liquid phase at 373 appearing in the above scheme are missing (k3a = k4 = K in the case of 2-methylbenzyl hydroperoxide forming

of 0), Walling [5], using the quasi-steady-state treatment in the long kinetic chain approximation, when it much more rapidly than o-tolualdehyde (V3 >> V3a and can be assumed that V = V , without using the αl >> β) [46]. The oxygen concentration limit in o -xylene 2 3 is reached at an oxygen concentration of [O2]top > xm, Journal substitution k6 = 2k52k7 [5,6,16] (as distinct from this w h ich corresponds to the third experimental point [46]. work), found that V2 = V3 is an irrational function of The oxygen concentration was calculated from the 2 Global x: a1x / b1x + c1x + d1 where a1, b1, c1, and d1 are oxygen solubility in liquid xylene at 373 K [61]. The coefficients. Again, this function has no maximum with following quantities were used in this mathematical respect to the concentration of any of the two

components. 8The oxygen concentration attained in the liquid may be below the

Thus, of the three kinetic models of oxidation thermodynamically equilibrium oxygen concentration because of mathematically analyzed above, which involve the diffusion limitations hampering the establishment of the gas–liquid radicals R• and RO • in three types of quadratic-law saturated solution equilibrium under given experimental conditions (for 2 example, when the gas is bubbled through the liquid) or because the chain termination reactions (reactions 5 –7) and are Henry law is violated for the given gas–liquid system under real variants of the conventional model [2,5,6,16,44,45], the conditions.

13 0

r ea

VI Fig. 4 : (1, 2) Quantum yields of (1, ●) hydrogen ue ersion I

s peroxide and (2, ○ ) water resulting from the photoche- s mical oxidation of hydrogen in the hydrogen–oxygen I system as a function of the oxygen concentration x (light wavelength of 171.9–172.5 nm, total pressure of 105 Pa, room temperature [64]). ( 3, 4 ) Hydrogen peroxide

forma tion rate V(H2O2) (dashed curves) as a function of

the rate V(H2O2) at which molecular oxygen is passed )

Fig. 3 : (1,¯) Reconstruction of the functional depen- through a gas-discharge tube filled with (3, Δ ) atomic ( dence of the 2-methylbenzyl hydroperoxide formation and (4, □) molecular hydrogen. Atomic hydrogen was rate V3(RO2H) on the dissolved oxygen concentration x obtained from molecular hydrogen in the gas-discharge from empirical data (points) using Eq. (3a) (model tube before the measurements (total pressure of 25–77

optimization with respect to the parameter α) for the Pa, temperature of 77 K [47]). The symbols represent Research Volume XIII o-xylene–oxygen system at 373 K [46] (standard experimental data. –7 deviation of SY = 5.37 × 10 . (2, □) Recons-truction of Scheme 4

the functional dependence of the total hydrogen Frontier Nonbranched-chain oxidation of hydrogen and peroxide formation rate V (H O ) on the dissolved 3 , 7 2 2 changes in enthalpy (ΔHo , kJ mol–1) for elementary oxygen concentration x from empirical data (symbols) 298 reactions9 using Eqs. (3a) and (12) with = 0 (model optimization

β Science with respect to the parameter α) for the γ-radiolysis of of water saturated with hydrogen and containing different 9According to Francisco and Williams [49], the enthalpy of formation –8 • • • • amounts of oxygen at 296 K [63] (SY=1.13 × 10 ). The (ΔHf˚298) in the gas phase of H , HO , HO 2, HO 4 (the latter without the possible intramolecular hydrogen bond taken into account), O3, dashed curve described V3(H2 O2) as a function of the H2O [2], H2O2, and H2O 4 is 218.0 ± 0.0, 39.0 ± 1.2, 12.6 ± 1.7, 122.6 Journal oxygen concentration x based on Eq. (3a) (model ± 13.7, 143.1 ± 1.7, –241.8 ± 0.0, –136.0 ± 0, and –26.0 ± 9 kJ mol– 1 optimization with respect to α) and the experimental , respectively. Calculations for the · HO4 radical with a helical structure –8 data of curve 2 (S = 1.73 × 10 ). were carried out using the G2(MP2) method [68]. The stabilization Y Global • • • energies of HO 2, HO 4, and HO 3 were calculated in the same work to ii. Addition of the Hydrogen Atom be 64.5 ± 0.1, 69.5 ± 0.8, and 88.5 ± 0.8 kJ mol–1, respectively. The types of the O4 molecular dimers, their IR spectra, and higher oxygen A number of experimental findings concerning oligomers were reported [69,70]. The structure and IR spectrum of the the autoinhibiting effect of an increasing oxygen hypothetical cyclotetraoxygen molecule O4, a species with a high concentration at modest temperatures on hydrogen energy density, were calculated by the CCSD method, and its enthalpy oxidation both in the gas phase [47,64,65] (Fig. 4) and of formation was estimated [71]. The photochemical properties of O4 in the liquid phase [63] (Fi g. 3, curve 2), considered in and the van der Waals nature of the O2–O2 bond were investigated [72,73]. The most stable geometry of the dimer is two O2 molecules our earlier work [66], can also be explained in terms of parallel to one another. The O4 molecule was identified by NR mass the competition kinetics of free radical addition [14,67]. spectrometry [74].

Chain initiation

h , γν o Н ¾¾ ®¾ Н• DН ± 1. 2 2 , 298 = 436.0 0.0. Chain propagation o k2 · DН • ¾®¾ 298 2. Н + О2 HO2 , = –205.4 ± 1.7;

k · 3 o 3. HO + Н ¾®¾ Н О + НО•, DН = –215.4 ± 2.9 2 2 2 298 • o (or Н2О2 + Н ), DН = 69.4 ± 1.7; 13 298 20 k • ¾'3 ®¾ • o 3 ¢. НО + Н2 Н2О + Н , DН 298 = –62.8 ± 1.2. ear

Y Inhibition

36 · k 4 · o О ¾®¾ DН ± 4. HO 2 + 2 HO 4 , 298 = 110.0 15.4.

Chain termination V 2 k • ¾¾®¾ 5 o VI 5. 2 Н ( + М ) Н2 ( + М ), DН 298 = –436.0 ± 0.0;

• · k 6 o 6. Н + HO ¾®¾ Н О + О , DН = –476.6 ± 13.7 4 2 2 2 298

(or: + , ∆  = –439.3 ± 15.4, Н2О О3 Н 298 o Н2 + 2О2), DН 298 = –340.6 ± 13.7;

) 2 k · ¾¾7 ®¾ o ( 7. 2 HO Н2О2 + 2О3, DН = –381.2 ± 27.4 4 298

o (or: Н2О + О3 + 2О2 , DН = –343.9 ± 29.1, 298

Research Volume XIII Issue ersion I o

Н2О2 + 2О3 , DН 298 = –95.0 ± 30.8,

Frontier Н О Н 2 + 4 2), D 298 = –245.2 ± 27.4.

• The hydroperoxyl free radical HO 2 [75–78] variant) and 3’ regenerate hydrogen atoms. It is • Science resulting from reaction (2) possesses an increased assumed [56,57] that the hydrotetraoxyl radical HO 4 (first reported in [79,80]) resulting from endothermic of energy due to the energy released the conversion of the O=O multiple bond into an HO–O• ordinary bond. reaction 4, which is responsible for the peak in the Therefore, before its possible decomposition, it can experimental rate curve (Fig. 2, curve 3), is closed into a

Journal • interact with a hydrogen or oxygen molecule as the third five-membered [OO–HO]··· cycle due to weak body via parallel (competing) reactions (3) and (4), intramolecular hydrogen bonding [54,81]. This structure • respectively. The hydroxyl radical HO that appears and imparts additional stability to this radical and makes it Global disappears in consecutive parallel reactions (3) (first least reactive. variant) and 3’ possesses additional energy owing to the • The HO 4 radical was discovered by Staehelin exothermicity of the first variant of reaction 3, whose et al. [82] in a pulsed γ-radiolysis study of ozone heat is distributed between the two products. As a degradation in water; its UV spectrum with an • consequence, this radical has a sufficiently high absorption maximum at 260 nm (ε(HO 4 )280 nm = 320 2 –1 • reactivity not to accumulate in the system during these ±15 m mol ) was reported. The spectrum of the HO 4 reactions, whose rates are equal ( V3 = V3¢ ) under quasi- radical is similar to that of ozone, but the molar • steady-state conditions, according to the above absorption coefficient ε(HO 4 )λmax of the former is almost scheme. Parallel reactions 3 (second, parenthesized two times larger [82]. The assumption about the cyclic

• 1 –1  1 + s tructure of the HO 4 radical can stem from the fact that a ∆ g ) = 94.3 kJ mol [20, 41] and ∆Н f 298 (О2, b Σg ) = its mean lifetime in water at 294 K, which is (3.6 ± 0.4) 161.4 kJ mol–1[41], which are deactivated by collisions, × 10–5 s (as estimated [66] from the value of 1/k for the and in the form of O3) and yield hydrogen peroxide or • k • reaction HO 4 ¾ ®¾ HO 2 + O2 [ 82]), is 3.9 times water via a nonchain mechanism, presumably through • longer than that of the linear HO 3 radical [68, 83] the intermediate formation of the unstable hydrogen estimated in the same way [66] for the same conditions 10 tetraoxide molecule H2O4 [61, 62]. Ozone does not –6 [84], (9.1 ± 0.9) × 10 s. MP2/6-311++G** calcula- interact with molecular hydrogen. At moderate tions using the Gaussian-98 program confirmed that the temperatures, it decomposes fairly slowly, particularly in cyclic structure of HO• [85] is energetically more 4 the presence of О ( Χ 3Σ− ) [41]. The reaction of ozone favorable than the helical structure [68] (the difference in 2 g –1 with Н• atoms, which is not impossible, results in their energy is 4.8–7.3 kJ mol , depending on the 3 10 • 1 0 computational method and the basis set). For replacement with НО radicals. The relative contributions 2 example, with the MP2(full)/6-31G(d) method, the from reactions 6 and 7 to the process kinetics can be roughly estimated from the corresponding enthalpy r difference between the full energies of the cyclic and ea

• increments (Scheme 2). Y acyclic HO 4 conformers with their zero-point energies When there is no excess hydrogen in the (ZPE) values taken into account (which reduces the 37 energy difference by 1.1 kJ mol–1) is – 5.1 kJ mol–1 and hydrogen–oxygen system and the homomolecular dimer • O4 [71–74,89,90], which exists at low concentrations the entropy of the acyclic-to-cyclic HO 4 transition is o –1 –1 (depending on the pressure and temperature) in ΔS 298 = –1.6 kJ mol K . Therefore, under standard • • equilibrium with O2 [7 0], can directly capture the H atom conditions, HO 4 can exist in both forms, but the cyclic • 12 V to yield the heteronuclear cluster HO 4 , which is more structure is obviously dominant (87%, Keq = 6.5) [85].

VI Reaction (4) and, to a much lesser degree, stable than O4 [70] and cannot abstract a hydrogen atom from the hydrogen molecule, nonchain hydrogen reaction (6) inhibit the chain process, because they lead ue ersion I s

oxidation will occur to give molecular oxidation products s to inefficient consumption of its main participants – HO• 2 via the disproportionation of free radicals. I and H•. The low-reactive hydrotetraoxyl radical HO• The hydrogen molecule that results from 4 [82], which presumably has a high energy density [71], reaction (5) in the gas bulk possesses an excess may be an intermediate in the efficient absorption and energy, and, to acquire stability within the approximation conversion of biologically hazardous UV radiation used in this work, it should have time for deactivation via energy the Earth upper atmosphere. The potential collision with a particle M capable of accepting the •

energy surface for the atmospheric reaction HO + O3, excess energy [87]. To simplify the form of the kinetic () in which the adduct HO • (2A) was considered as an equations, it was assumed that the rate of the 4 bimolecular deactivation of the molecule substantially intermediate, was calculated by the DMBE method [91]. exceeds the rate of its monomolecular decomposition, From this standpoint, the following reactions are Research Volume XIII which is the reverse of reaction 5 [2]. possible in the upper troposphere, as well as in the lower and middle stratosphere, where most of the ozone Reactions 6 and 7 (taking into account the layer is situated (altitude of 16 –30 km, temperature of

principle of detailed balance for the various pathways) 4 3 ( 217–227 K, pressure of 1.0 × 10 –1. 2 × 10 Pa [92]; the Frontier 3 − regenerate hydrogen and oxygen (in the form of О2( Χ Σ o g corresponding ΔH 298 reaction values are given in kJ  mol–1 [49]): molecules, including the singlet states with ∆Н f 298 (О2, Science

• • of Н2О (vapor) + hn ® Н + HO [ 92 ]; (8) • · o НО + O3 ® HO4 [ 80,82,91] , Н 298 = –59.5; (9) · · - o ® Χ 3 S [ ] Н Journal HO 4 HO2 + O2( g ) 82,91 , 298 = –110.0 (10) · o 1D DН (or HO 2 + O2( a g), 298 = –15.7. Global

10 11 • There were calculations for the two conformers (cis and trans) of the The planar, six-atom, cyclic, hydrogen-bonded dimer (HO 2 )2 was • HO4 radical [86] using large scale ab initio methods and density calculated using quantum chemical methods (B3LYP density functional theory) [88]. The hydrogen bond energy is 47.7 and 49.4 kJ functional techniques with extended basis sets. Both conformers have mol–1 at 298 K for the triplet and singlet states of the dimer, a nearly planar geometry with respect to the four oxygen atoms and present an unusually long central O–O bond. The most stable respectively. • 12 conformer of HO 4 radical is the cis one, which is computed to be It is impossible to make a sharp distinction between the two-step • 2 3 - endothermic with respect to HO (X A”) + O (X S g ) at 0 K. bimolecular interaction of three species via the equilibrium formation of 2 2 the labile intermediate O4 an d the elementary termolecular reaction O2 • • +O2 +H → HO4 .

• The HO 4 radical can disappear via dispropor- O dimer, К = k/k’ is the equilibrium constant of the 4 eq tionation with a molecule, free radical, or atom in k • addition to dissociation. Note that emission from O2 reversible reaction 2O2 Û O4 with k’ >> kadd[H ]). The 1 1 + ( a Δg ) and O2( b S g ) is observed at altitudes of 30–80 k ' and 40–130 km, respectively [93]. formation rates of the stable products of nonchain

Staehelin et al. [82] pointed out that, in natural oxidation (k3 = 0), provided that either reactions (2) and

systems in which the concentrations of intermediates (4) or reaction (2) alone (k4 = 0) occurs (Scheme 4; in • are often very low, kinetic chains in chain reactions can the latter case, reactions 6 and 7 involve the HO 2 • be very long in the absence of scavengers since the radical rather than HO 4 ), are given by modified Eqs. rates of the chain termination reactions decrease with (11) and (12) with β = 0, (αl + x) replaced with 1, and х2 decreasing concentrations of the intermediates replaced with х. 13 according to a quadratic law, whereas the rates of the Note that, if in Scheme 4 chain initiation via 20 chain propagation reactions decrease according to a reaction 1 is due to the interaction between molecular hydrogen and molecular oxygen yielding the hydroxyl ear linear law. Y The kinetic description of the noncatalytic radical HO• in stead of H• atoms and if this radical

38 oxidation of hydrogen, including in an inert medium [87], reacts with an oxygen molecule (reaction 4) to form the • in terms of the simplified scheme of free-radical hydrotrioxyl radical HO 3 (which was obtained in the gas nonbranchedchain reactions (Scheme 4), which phase by neutralization reionization (NR) mass considers only quadratic-law chain termination and spectrometry [83] and has a lifetime of >10–6 s at 298 K) ignores the surface effects [47], at moderate and chain termination takes place via reactions 5–7 V • • • temperatures and pressures, in the absence of involving the HO and HO 3 , radicals instead of H and • VI transitions to unsteady-state critical regimes, and at a HO4 , respectively, the expressions for the water chain substantial excess of the hydrogen concentration over formation rates derived in the same way will appear as a the oxygen concentration was obtained by means of rational function of the oxygen concentration x without a

quasi-steady-state treatment, as in the previous studies maximum: V ’(H O) = V k ’l (k x + 2k V ). 3 2 1 3 4 5 1 on the kinetics of the branched-chain free-radical Curve 2 in Fig. 3 describes, in terms of the

oxidation of hydrogen [76], even though the applicability overall equation V =V x(alf + x 3) f 2 for the rates of 3, 7 1 m m of this method in the latter case under unsteady states reactions 3 and 7 (which was derived from Eqs. 3a and conditions was insufficiently substantiated. The method 4 2 12, respectively, the latter in the form of V7 =V1x / f m ) 13 = (12a) [96] in which k2 is replaced with its analytical was used with the following condition: k6 2k52k7 ( expression derived from Eq. (8) with β = 0 everywhere), ( see Introduction). The equation for the rate of the chain the dependence of the hydrogen peroxide formation formation of hydrogen peroxide and water, V3(H2O2; –8 –3 –1 ¢ rate (minus the rate VH O = 5.19 × 10 mol dm s of H2O) = V3’(H2O), via reactions 3 and 3 is identical to Eq. 2 2

(3, 3a) with the corresponding analytical expression for the primary formation of hydrogen peroxide after Research Volume XIII Issue ersion I completion of the reactions in spurs) on the initial k2. The ratio of the rates of the competing reactions is concentration of dissolved oxygen during the - V3/V4 = αl/x, and the chain length is v = V3/V1. The rates γ –4 of nonchain formation of hydrogen peroxide and water radiolysis of water saturated with hydrogen (7 × 10 Frontier mol dm–3) at 296 K [63]. These data were calculated in via reactions (6) and (7) – quadratic-law chain termination - are identical to Eqs. (11) and (12) provided the present work from the initial slopes of hydrogen 60 that β = 0. In these equations, l and x are the molar peroxide buildup versus dose curves for a Co Science γ-radiation dose rate of Р = 0.67 Gy s–1 and absorbed concentrations of hydrogen and oxygen (l >> x), lm and

of doses of D @ 22.5–304.0 Gy. The following values of the xm are the respective concentrations at the maximum point of the function, V1 is the rate of initiation (reaction 13 2 For example, the ratio of the rate constants of the bimolecular 1), α = k3 /k4, the rate constant k2 = alm 2k5V1 / x m disproportionation and dimerization of free radicals at room Journal • • • • 0.5 is derived from the condition ∂V3/∂x = 0, and 2k5 is the temperature is k(HO + HO 2 )/[2k (2HO )2k(2HO 2 )] = 2.8 in the rate constant of reaction 5 (hydrogen atom recom- atmosphere [92] and k(H• + HO•)/[2k(2H •)2k(2HO•)]0.5 = 1.5 in water [94]. These values that are fairly close to unity. bination), which is considered as bimolecular within the 14 Global 14 This rate constant in the case of the pulsed γ-radiolysis of ammonia– given approximation. oxygen (+ argon) gaseous mixtures at a total pressure of 105 Pa and a In the case of nonchain hydrogen oxidation via temperature of 349 K was calculated to be 1.6 × 108 dm3 mol–1 s–1 • k add • [65] (a similar value of this constant for the gas phase was reported in the above addition reaction (H + O4 ¾ ¾ ®¾ HO 4 ), an earlier publication [95]). Pagsberg et al. [65] found that the the formation rates of the molecular oxidation products • dependence of the yield of the intermediate HO on the oxygen concentration has a maximum close to 5 × 10–4 mol dm–3. In the in reactions 6 and 7 (Scheme 4, k2 = k3 = k4 = 0) are defined by modified Eqs. (11) and (12) in which β = 0, computer simulation of the process, they considered the strongly exothermic reaction HO • + NH ® H O + •NHOH, which is similar to 2 3 2 (αl + x) is replaced with 1, and k2 is replaced with kaddKeq reaction 3 in Scheme 4, whereas the competing reaction 4 was not • (k K is the effective rate constant of H addition to the taken into account. add eq

© 2013 Global Journals Inc. (US) Kinetics of Nonbranched-Chain Processes of the Free-Radical Addition with Reactions, in Which the 1:1 Adduct Radicals Compete for Interaction with Saturated and Unsaturated Components of the Binary Reaction System primary radiationchemical yield G (species per 100 eV of · k · 3b. R R А ¾+ ¾ 3b® R А + R . energy absorbed) for water γ-radiolysis products in the 14 14 bulk of solution at pH 4–9 and room temperature were Inhibition used (taking into account that V = GP and V1 = GHP): For addition to an olefin or CH2O, GH2O2 = 0.75 and GH = 0.6 (initiation yield; see Conclusions) [94]; V = 4.15 × 10–8 mol dm–3 s–1; 2k = · k4 · 1 5 4. RR В ¾+ ¾ ® R В + R ; 2.0 × 1010 dm3 mol–1 s–1 [94]. As can be seen from Fig. 23 23

3, the best description of the data with an increase in the for addition to О2, oxygen concentration in water is attained when the rate V of the formation of hydrogen peroxide via the · k4а · 7 4a. RR 23 В ¾+ ¾ ® R 2а . nonchain mechanism in the chain termination reaction 7 –2 3 (curve 1, α = (8.5 ± 2) × 10 ) is taken into account in Chain termination 1 0 addition to the rate V of the chain formation of this 2 3 · 2 k product via the propagation reaction 3 (dashed curve 2, 5. 2R ¾ ¾5®¾ Prod; r 1 ea

α = 0.11 ± 0.026). The rate constant of addition Y ·· k reaction 2 determined from α is substantially ¾+ ¾ 6® 7 10 6. 1 RR 2(2a) Prod ; 39 underestimated: k2 = 1.34 × 10 (vs 2.0 × 10 [94]) dm3 mol–1 s–1. The difference can be due to the fact that · 2 k the radiation-chemical specifics of the process were not 7. R2 ¾ ¾7®¾ Prod . 2(2a) considered in the kinetic description of the experimental data. These include oxygen consum ption via reactions In this scheme, I is the initiator, for example, a V • that are not involved in the hydrogen oxidation scheme peroxide [5,17,18,29,30]; R 0 is any reactive radical VI [66,97,98] and reverse reactions resulting in the (initiator); A is an atom of hydrogen [2,5,6,17,18,22– ue ersion I s decomposition of hydrogen peroxide by intermediate 24,29–32] or halogen [2,5,19–21]; B is an atom of s

- • • I products of water γ-radiolysis (eaq , H , HO ), with the hydrogen [5,17–21,23,24,29–32], halogen [22], or - • major role played by the hydrated electron e aq [94]. oxygen (in oxidation) [2,5 6,16,44–46]; R 1 is a radical • • d) General Scheme of the Free-Radical Addition to such as PCl2 [19], CCl3 [20], an alkyl [2,5,6,21], a 1-

Olefins, Formaldehyde, and Oxygen hydroxyalkyl [5,6,17,22–24,29,32], or a similar functiona- • The general scheme of the nonbranched-chain lized radical [5] (addend); R 2 is the formyl 8,9,29], an addition of a free radical from a saturated compound to alkenyl (propenyl or higher) [2 5,17–22], a 1-hydrox-

yalkenyl [5,17,18,23,24], or a similar functionalized low- an olefin (and its functionalized derivative), () formaldehyde, or dioxygen in liquid homogeneous reacrtive radical [5,18] (inhbitor) or the oxygen atom (in • binary systems of these components includes the oxidation) [2,5,6,13,14,16,44 –46,56,57,96–98]; R 2a is • following reactions [57,97,98]. the low-reactive alkyltetraoxyl 1:2 adduct radical RO 4

• Research Volume XIII [13,14,56,57,96–98] (inhibitor); R 3 is the active 1:1 Scheme 5 • adduct radical; R 4 is an active fragment radical, such as Initiation hydroxymethyl [8,9,12,29,32 ], an alkoxyl radical, or

Frontier 2 k · hydroxyl (in oxidation) [2,5,6,13,14,16,44,46,56,57,96– 1. I ¾ 1®¾ R2 ; 0 98]; R0A, R0B, R1A, and R4A are saturated molecules;

R2B is an unsaturated molecule, viz., an olefin · k a1 ·

[2,5,11,17–22], formaldehyde [8,9,12,29–32], or dioxy- Science 1a. R R 10 А ¾+ ¾® R А + R10 ; gen (in oxidation) [2,5,6,13,14,16,44–46,56,57,96–98];

of for addition to an olefin at comparable component R'R''CO is a carbonyl compound viz., aldehyde concentrations, [2,6,8,9,12,14,29–32,44] or ketone [2,6,14,29,32,44]; · R A and R B are molecular products (1:1 adducts); and · k1b 3 3 Journal 1b. R BR ¾+ ¾ ® BR + R . 0 2 0 2 Prod stands for molecular products of the dimerization and disproportionation of free radicals. Chain propagation

The chain evolution stage of Scheme 5 include Global · k2 · consecutive reactions 2, 3; 2, 3a; and 3a, 3b; parallel 2. RR 21 В ¾+ ¾ ® R3 ; (competitive) reactions 3, 3a; 3, 3b; 3, 4 (or 4a); and 3a, · k3 · 4 (or 4a); and consecutive-parallel reactions 2 and 4 (or 3. RR 13 A ¾+ ¾ ® R + RA 13 ; 4a). Addition to olefins is described by reactions 1–3, 4, and 5–7 and the corresponding rate equations (1)–(4a). for addition to O2 and the 1-hydroxyalkyl radical to

CH2O, Addition to the carbonyl carbon atom of the free (unsolvated) form of formaldehyde is represented by · k · 3а reactions 1, 1a, 2–4 (the main products are a 1,2- 3a. R3 ¾ ®¾ R¢R ¢¢ CO + R4 ;

alkanediol, a carbonyl compound, and methanol), and V3, 4 = (V1/j)[(αl/x) + 1], (14) 5–7 and is described by Eqs. (5) and (6). In the case of

hydroxymethyl addition, the process includes reactions where j = 1 under conditions (a) and (b) and j = 2 at

1, 1a, 2, 3, 5a, 4 (the main product is ethanediol), and 2 the point of maximum (where k2x (α + x) 2k5V1). 5–7 and is described by Eq. (7). If the nonchain 2 Equations (8) and (9) under the condition k2x >> (αl + formation of ethanediol in reaction 5 is ignored, the ≅ + ) 2k V (descending branch of a peaked curve) process is described by Eq. (5). Addition to the oxygen β x 5 1 can be transformed into Eqs. (15) and (16), respectively, molecule is described by reactions 1, 1a, 2–3b, 4a (the which express the simple, inversely proportional main products are an alkyl hydroperoxide, alcohols, dependences of reaction rates on and provide carbonyl compounds, and water), and 5–7 and Eqs. (8), x tentative estimates of and : (8a), (9), and (9a). α β 13

20 The main molecular products of the chain V3 = V1αl /jx, (15) process – R3A, R’R”CO, and R4A – result from reactions ear 3, 3a, and 3b – chain propagation through the reactive V = V β /jx, Y 3а 1 (16) • • free radical R 1 or R 4 , R'R''CO. The competing reaction where j = 2 at the point of maximum (where k 2 ( 40 4, which opposes this chain propagation, yields the by- 2 x αl product R3B a nonchain mechanism. The rate of + β+ x) 2k5V1 ) a nd j = 1 for the descending branch of formation of the products is a complicated function of ≅ the curve. Equation (3) for V 3, 4 under condition (b) the formation rates (V3a = V3b) and disappearance rates transforms into Eq. (15). • • V of the free radicals R 1 and R 2(2a): V(R3A, R’R”CO, R4A, For radiation-chemical processes, the rates V in R3B) = V2 = V3 + V3a + V4(4а) = (V1a + V3 + V3b – V5) – VI the kinetic equations should be replaced with radiation- (V1b + V4(4а) – V7). The rates of reactions 5–7 at k1b = 0 chemical yields G using the necessary unit conversion ([R1A] >> [R2B]) are given by Eqs. (9)–(11). The rate factors and the relationships V = GP and V1 = e1G ratios of the competing reactions are V3/V4(4а) = αl/x and • (R 1) P, where P is the dose rate, e1 is the electron fraction V3а/V4(4а) = β/x (where α = k3/k4(4а), β = k3а/k4(4а) mol –3 of the saturated component R1A in the reaction system dm , and l and x are the molar concentrations of the • [100], and G(R 1 ) is the initial yield of the chain-carrier reactants R1A and R2B, respectively), and the chain free radicals (addends) – initiation yield [39,94]. length is v = (V3 + V3a)/V1. Unlike the dependences of The optimum concentration of the unsaturated the rates of reactions 4a (or 4 at k1b = 0, with V4(4a) ≤

) component in the system maximizing the process rate, V ), 5, and 7 (Eqs. (9), (10), and (12)), the dependences 1 xm, can be calculated using rate equations (3a), (4a), ( of the rates V of reactions 3, 3a,b, 4 (at k1b ≠ 0), and 6 (8a), and (9a) or the corresponding analytical (Eqs. (1)–(9a) and (11)) on x have a maximum. Reaction expressions for k2 prov ided that the other parameters 1b, which competes with reaction 1a, gives rise to a involved in these equations are known. This opens up maximum in the dependence described by Eq. (2), Research Volume XIII Issue ersion I the way to intensification of some technological whereas reaction 4 or 4a, competing with reactions 3 proce sses that are based on the addition of free radicals and 3a,b, is responsible for the maxima in the to C=C, C=O, and O=O bonds and occur via a dependences defined by Eqs. (1), (3)–(7) or (8, 8a) and

Frontier •15 • nonbranched -chain mechanism through the formation of (9, 9a). The low -reactive radicals R 2 and R 2a , resulting a 1:1 adduct. from reactions 4 and 4a, inhibit the nonbranched-chain • addition of R 1 to olefins (or formaldehyde) and II. Conclusions Science dioxygen, respectively. Reaction 4a leads to non- • The above data concerning the competition of productive loss of R adduct radicals. 3 kinetics of the nonbranched-chain addition of saturated For approximate estimation of the parameters of free radicals to the multiple bonds of olefins (and its the kinetic equations (3), (4), (8), and (9), Eq. (4) under derivatives), formaldehyde, and oxygen molecules make Journal 2 the conditions (a) k2x << (αl + x) 2k5V1 (ascending it possible to describe, using rate equations (1)–(9a),

branch of a peaked curve) and (b) k x2 >> (αl + x) obtained by quasi-steady-state treatment, the peaking 2 Global experimental dependences of the formation rates of 2k V ( descending branch) is transformed into simple 5 1 molecular 1:1 adducts on the initial concentration of the functions (direct and inverse proportionality, unsaturated compound over the entire range of its respectively) of the concentration x of the unsaturated variation in binary systems consisting of saturated and compound. These functions allow tentative estimates of unsaturated components (Figs. 1–3). In such reaction the parameters k2 and α to be derived from the experimental product formation rate V provided that V 1 15The stabilization energy of the low-reactive free radicals and 2k5 are known: CH2=C(CH3 )ĊH2, CH2=CH Ċ HOH, and H Ċ= O in the standard state in the gas phase is –52.0, –42.1, and –24.3 kJ mol–1, respectively [4,99]. V3, 4 = V k 21 j 2kx 5 (13)

systems, the unsaturated compound is both a reactant and Formaldehyde”, Kinetics and Katalysis, 1994, and an autoinhibitor, specifically, a source of low- vol. 35, no. 4, pp. 509–513. reactive free radicals shortening kinetic chains. The 10. M. M. Silaev, “Competition Kinetics of Nonbranched progressive inhibition of the nonbranched -chain Chain Processes of Free-Radical Addition to Double

processes, which takes place as the concentration of Bonds of Molecules with the Formation of 1:1 the unsaturated compound is raised (after the maximum Adducts”, Kinetica i Kataliz., 1999, vol. 40, no. 2, pp. process rate is reached), can be an element of the self- 281–284, English Translation in: Kinetics and regulation of the natural processes that returns them to Catalysis, 1999, vol. 40, no. 2, pp. 256–259. the stable steady state. 11. M. M. Silaev, “Simulation of the Nonbranched-Chain A similar description is applicable to the Addition of Saturated Free Radicals to Alkenes and nonbranched -chain free-radical hydrogen oxidation in Their Derivatives Yielding 1:1 Adducts”, Teoreti- 3 1 0 water at 296 K [63] (Fig. 3, curve 2). Using the hydrogen cheskie Osn-ovy Khimicheskoi Tekhnologii, Vol. 41, oxidation mechanism considered here, it has been No. 3, 2007, pp. 280 –295, English Translation in: 2 demonstrated that, in the Earth’s upper atmosphere, the r Theoretical Foundations of Chemical Engineering, ea

• Y decomposition of O3 in its reaction with the HO radical 2007, vol. 41, no. 3, pp. 273–278. can occur via the addition of the latter to the ozone 12. M. M. Silaev, “Simulation of Nonbranched Chain 41 • molecule, yielding the HO 4 radical, which is capable of Processes for Producing 1,2-Alkanediols in Alcohol– efficiently absorbing UV radiation [82]. Formaldehyde Systems”, Teoreticheskie Osnovy Khimicheskoi Tekhnologii, 2007, vol. 41, no. 4, pp. References Références Referencias 379–384, English Translation in: Thoretical V 1. L. V. Gurvich, G. V. Karachevtsev, V. N. Kondrat'ev, Foundations Chemical Engineering, 2007, vol. 41, Yu. A. Lebedev, V. A. Medvedev, V. K. Potapov, and no. 4, pp. 357–361. VI

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21. V. E. Myshkin, A. G. Shostenko, P. A. Zagorets, K. Solutions in C1-C3 Alkanols”, Khimiya Vysokich G. Markova, and A. I. Pchelkin, “Determination of Energii, Vol. 38, No. 4, 2004, pp. 270–272, English Absolute Rate Constants for the Addition of the Translation in: High Energy Chemistry, Vol. 38, No. Ethyl Radical to Olefins”, Teoreticheskaya i 4, 2004, pp. 236–238. Eksperimental’naya Khimiya, Vol. 13, No. 2, 1977, 34. I. Novoselov, M. M. Silaev, and L. T. Bugaenko, pp. 266–271. “Depen dence of Ethanediol Yield on Formaldehyde 22. R. A. Zamyslov, A. G. Shostenko, I. V. Dobrov, and Concentration in γ-radiolysis of Methanol– N. P. Tarasova, “Kinetics of γ-Radiation-Induced Formaldehyde System at 373–473 K”, Khimiya Reactions of 2-Propanol with Trifluoropropene and Vysokikh Energii, Vol. 42, No. 1, 2008, pp. 74–75, Hexaflu-oropropene”, Kinetika i Katalyz., Vol. 28, No. English Translation in: High Energy Chemistry , vol. 4, 1987, pp. 977–979. 42, no. 1, 2008, pp. 69–70. 13 23. M. M. Silaev, “Dependence of Radiation-chemical 35. I. Novoselov, M. M. Silaev, and L. T. Bugaenko, “γ- 20 γ-Diol Yields on the 2-Propen-1-ol Concentration in Induced Single-Step Synthesis of Ethylene Glycol from Methanol–Formaldehyde Solution”, Theoreti- ear the γ-radiolysis of Aliphatic Saturated C1-C3 Alcohol Y + 2-Propen-1-ol Systems”, Khimiya Vysokikh cheskie Osnovy Khimicheskoy Tekhnologii, Vol. 44 ,

42 Energii, Vol. 24, No. 3, 1990, pp. 282–283. No. 4, 2010, pp. 450–453, English Translation in: 24. M. M. Silaev, “γ-Diol Formation via the Autooxidation Theoretical Foundation of Chemical Engineering, of 2-Propen-1-ol Solutions in Saturated Alcohols”, Vol. 44, No. 4, 2010, pp. 432–435. Vestnik Moskovskogo Universiteta, Ser. 2: Khimiya, 36. I. Novoselov, M. M. Silaev, and L. T. Bugaenko, Vol. 35, No. 1, 1994, pp. 40–42. “Dependence of 1,2-Propanediol Yield on V 25. L. T. Bugaenko, M. G. Kuzmin, and L. S. Polak, Formaldehyde Concentration in γ-radiolysis of

VI “High-Energy Chemistry”, Horwood Hall, New York, Ethanol– Formaldehyde System at 373473 K”, 1993, p. 112. Khimiya Vysokikh Energii, Vol. 41, No. 1, 2007, p. 58, 26. J. K. Thomas, “Pulse γ-radiolysis of Aqueous English Translation in: High Energy Chemistry, Vol. Solutions of Methyl Iodide and Methyl Bromide. The 41, No. 1, 2007, p. 53. Reactions of Iodine Atoms and Methyl Radicals in 37. S. Ya. Pshezhetskii, A. G. Kotov, V. K. Milinchuk, V. Water” The Journal of the Physical Chemistry , Vol. A. Roginskii, and V. I. Tupikov, “EPR svobodnykh 71, No. 6, 1967, pp. 1919–1925. radikalov v radiatsionnoi khimii” (“ESR of Free 27. S. K. Ogorodnikov, Formal'degid (Formaldehyde), Radicals in Radiation Chemistry”), Khimiya,

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Polarity of Solvents, and Total Concentration of No. 9, 1993, p. 1944. Research Volume XIII Issue ersion I Formaldehyde in Solution”, Zhurnal Fizicheskoi 39. M. M. Silaev, “Applied Aspects of the -radiolysis of γ Khimii, Vol. 53, No. 7, 1979, pp. 1647–1651. C1-C4 Alcohols and Binary Mixtures on Their Basis”,

29. Oyama, M., “A Free-Radical Reaction of Primary Khimiya Vysokikh Energii, Vol. 36, No. 2, 2002, pp.

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Journal of Organic Chemistry, Vol. 30, No. 7, 1965, Chemistry, Vol. 36, No. 2, 2002, pp. 70–74. pp. 2429–2432. 40. M. M. Silaev, L. T. Bugaenko, and E. P. Kalyazin,

Science 30. G. I. Nikitin, D. Lefor, and E. D. Vorob’ev, “Free “On the Possibility of Adequately Estimating the Radical Reaction of Primary Alcohols with of Rate Constants for the Reaction of Hydroxyalkyl Formaldehyde”, Izvestiya Akademii Nauk SSSR, Ser. Radicals with Each Other Using the Self-Diffusion Khimiya, No. 7, 1966, pp. 1271–1272. Coefficients or Viscosities of the Corresponding 31. M. B. Dzhurinskaya, A. V. Rudnev, and E. P. Journal Alcohols”, Vestnik Moskovskogo. Univiversiteta, Ser. Kalyazin, “High Temperature UV Photolysis of 2: Khimiya, Vol. 27, No. 4, 1986, pp. 386–389. Formaldehyde in Liquid Methanol”, Vestnik 41. O. I. Shadyro, “Radiation-chemical Conversions of Global Moskovskogo Universiteta, Ser. 2: Khimiya, Vol. 25, Aldehydes in Various Systems”, Ph.D. Thesis No. 2, 1984, pp. 173–176. (Chemistry), Belarusian State University, Minsk, 32. 32. E. P. Kalyazin, E. P. Petryaev, and O. I Shadyro, 1975. “Reaction between Oxyalkyl Radicals and 42. M. M. Silaev, “Relative Reactivity of α-Hydroxyethyl Aldehydes”, Zhurnal Organicheskoi Khimii, Vol. 13, Radicals for 2-Propene-1-ol and Formaldehyde No. 2, 1977, pp. 293–295. Double-Bond Addition”, Vestnik Moskovskogo 33. A. I. Novoselov, A.I., Silaev, M.M., and L. T. Universiteta, Ser. 2: Khimiya, Vol. 34, No. 3, 1993, Bugaenko, “Effect of Temperature on the Yields of p. 311. Final Products in the γ-radiolysis of Formaldehyde

43. H. Seki, R. Nagai, and M. Imamura, “γ-radiolysis of 54. G. C. Pimentel and A. L. McClellan, “The Hydrogen a Binary Mixture of Methanol and Water. The Bond” , L. Pauling, Editor, Freeman, San Francisco, Formation of Formaldehyde in the -radiolysis of γ 1960, p. 200. Liquid Methanol”, Bulletin of the Chemical Society of 55. G. A. Russell, “Deuterium -Isotope Effects in the Japan., Vol. 41, No. 12, 1968, pp. 2877–2881. Autooxidation of Aralkyl Hydrocarbons: Mechanism 44. V. Ya. Shtern, “Mekhanizm okisleniya uglevodorodov of the Interaction of Peroxy Radicals”, Journal of the v gazovoi faze (Mechanism of the Gas-Phase American Chemical Society, Vol. 79, No. 14, 1957, Oxidation of Hydrocarbons)”, Akademiya Nauk pp. 3871–3877. SSSR, Moscow, 1960. 56. M. M. Silaev, “The Competition Kinetics of 45. H. L. J. Bäckström, “Der Kettenmechanismus bei Nonbranched Chain Processes of Free-Radical der Autoxydation von Aldehyden”, Zeitschrift für Addition to Double Bonds of Molecules with the 3 1 0

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VI Society, Vol. 70, No. 11, 1948, pp. 3651–3655. of Singlet Oxygen by Oxygen- and Sulfur-Centered

48. A. L. Buchachenko, “Kompleksy radikalov i ue ersion I Radicals: Evidence for Energy Transfer to Peroxy s

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Vol. 20, No. 6, 1988, pp. 455–466. () 3386–3388. 50. V. N. Kokorev, N. N. Vyshinskii, V. P. Maslennikov, I. 60. N. N. Semenov, “Tsepnye reaktsii” (“Chain A. Abronin, G. M. Zhidomirov, and Yu. A. Reactions”), Goskhimtekhizdat, Leningrad, 1934, Aleksandrov, “Electronic Structure and Chemical pp. 241, 203. Research Volume XIII Reactions of Peroxides: I. MINDO/3 Calculation of 61. M. Reznikovskii, Z. Tarasova, and B. Dogadkin, the Geometry and Enthalpy of Formation of the “Oxygen Solubility in Some Organic Liquids”, Ground States of Organic and Organoelement

Zhurnal Obshchei Khimii, Vol. 20, No. 1, 1950, pp. Frontier Peroxides”, Zhurnal Strukturnoi Khimii, Vol. 22, No. 63–67. 4, 1981, pp. 9–15. 62. J. A. Howard and K. U. Ingold, “Absolute Rate 51. A. F. Dmitruk, V. V. Lobanov, and L. I. Kholoimova,

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of Peroxy Radical Recombination”, Teoreticheskaya of Journal of Chemistry , Vol. 45, No. 8, 1967, pp. i ksperimental’naya Khimiya, Vol. 22, No. 3, 1986, 793–802. pp. 363–366. 63. N. F. Barr and A. O. Allen, “Hydrogen Atoms in the

γ Journal 52. V. A. Belyakov, R. F. Vasil'ev, N. M. Ivanova, B. F. Minaev, O. V. Osyaeva, and G. F. Fedorova, -radiolysis of Water”, The Journal of Physical Chemistry, Vol. 63, No. 6, 1959, pp. 928–931. “Electronic Model of the Excitation of 64. H. A. Smith and A. Napravnik, “Photochemical Global Chemiluminescence in the Oxidation of Organic Oxidation of Hydrogen”, Journal of the American Compounds”, Izvestiya Akademii Nauk SSSR, Ser.: Fizika, Vol. 51, No. 3, 1987, pp. 540–547. Chemistry Society, Vol. 62, No. 1, 1940, pp. 385–393. 53. P. Ase, W. Bock, and A. Snelson, “Alkylperoxy and 65. P. B. Pagsberg, J. Eriksen, and H. C. Christensen, Alkyl Radicals. 1. Infrared Spectra of CH 3O2 and “Pulse γ-radiolysis of Gaseous Ammonia–Oxygen CH3O4CH3 and the Ultraviolet Photolysis of CH3O2 in Mixtures”, The Journal of Physical Chemistry, Vol. Argon + Oxygen Matrices”, The Journal of Physical 83, No. 5, 1979, pp. 582–590. Chemistry, Vol. 90, No. 10, 1986, pp. 2099 –2109.

66. M. M. Silaev, “Competitive Mechanism of the Non- HO2 Radical in the Gas Phase”, The Journal of branched Radical Chain Oxidation of Hydrogen Chemical Physics, Vol. 56, No. 9, 1972, pp. 4426– Involvingthe Free Cyclohydrotetraoxyl Radical 4432. • [OO···H···OO] , Which Inhibits the Chain Process”, 79. J. B. Robertson, “A Mass Spectral Search for H2O4 “Khimiya Vysokikh Energii, Vol. 37, No. 1, 2003, pp. and HO4 in a Gaseous Mixture Containing HO2 and O ”, Chem. & Ind., 1954, no. 48, p. 1485. 27–32, English Translation in: High Energy 2 Chemistry, Vol. 37, No. 1, 2003, pp. 24–28. 80. Bahnemann and E. J. Hart, “Rate Constants of the 67. M. M. Silaev, “Simulation of Initiated Nonbranched Reaction of the Hydrated Electron and Hydroxyl Chain Oxidation of Hydrogen: Oxygen as an Radical with Ozone in Aqueous Solution”, The Autoinhibitor”, Khimiya Vysokich Energii, Vol. 42, No. Journal of Physical Chemistry, Vol. 86, No. 2, 1982, 13 2, 2008, pp. 124–129, English Translation in: High pp. 252–255. 20 Energy Chemistry, Vol. 42, No. 1, 2008, pp. 95–100. 81. “Vodorodnaya svyaz’: Sbornik statei” (“The Hydrogen Bonding: Collection of Articles”) N. D.

ear 68. D. J. McKay and J. S. Wright, “How Long Can You

Y Make an Oxygen Chain?”, Journal of the American Sokolov, Editor, Nauka, Moscow, 1981. 82. J. Staehelin, R. E. Bühler, and J. Hoigné, “Ozone 44 Chemistry Society, Vol. 120, No. 5, 1998, pp. 1003-1013. Decomposition in Water Studied by Pulse γ- 69. N. P. Lipikhin, “Dimers, Clusters, and Cluster Ions of radiolysis. 2. OH and HO4 as Chain Intermediates”, Oxygen in the Gas Phase”, Uspekhi Khimii, Vol. 44, The Journal of Physical Chemistry, Vol. 88, no. 24, No. 8, 1975, pp. 366–376. 1984, pp. 5999–6004. V 70. S. D. Razumovskii, “Kislorod – elementarnye formy i 83. F. Cacace, G. de Petris, F. Pepi, and A. Troiani,

VI svoistva” (“Oxygen: Elementary Forms and “Experimental Detection of Hydrogen Trioxide”, Properties”), Khimiya, Moscow, 1979. Science, Vol. 285, No. 5424, 1999, pp. 81–82. 71. K. M. Dunn, G. E. Scuceria, and H. F. Schaefer III, 84. R. F. Bühler, J. Staehelin, and J. Hoigné, “Ozone “The infrared spectrum of cyclotetraoxygen, O4: a Decomposition in Water Studied by Pulse γ- – – theoretical investigation employing the single and radiolysis. 1. HO2/O 2 and HO3/O3 as Intermedia- double excitation coupled cluster method”, The tes”, The Journal of Physical Chemistry, Vol. 88, No.

Journal of Chemical Physics, Vol. 92, No. 10, 1990, 12, 1984, pp. 2560–2564. pp. 6077–6080. 85. V. Trushkov, M. M. Silaev, and N. D. Chuvylkin, • ) 72. L. Brown and V. Vaida, “Photoreactivity of Oxygen “Acyclic and Cyclic Forms of the Radicals HO4 , CH O• , and C H O• : Ab Initio Quantum Chemical

( Dimers in the Ultraviolet”, The Journal of Physical 3 4 2 5 4 Chemistry, Vol. 100, No. 19, 1996, pp. 7849–7853. Calculations”, Izvestiya Akademii Nauk, Ser.: 73. V. Aquilanti, D. Ascenzi, M. Bartolomei, D. Khimiya, No. 3, 2009, pp. 479-482, English Cappelletti, S. Cavalli, M. de Castro-Vitores, and F. Translation in: Russian Chemical Bulletin,

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VI Neftekhimiya, Vol. 40, No. 1, 2000, pp. 33–40, ue ersion I

English Translation in: Peroleum Chemistry, Vol. 40, s s

No. 1, 2000, pp. 29–35. I

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