Kinetics and Mechanism of Reactions of Aliphatic Stable Nitroxide Radicals in Chemical and Biological Chain Processes

1. Introduction

Stable nitroxide radicals (>NO^•) play very important role in experimental studies and in theoretical analysis of chemical and biochemical processes’ mechanism for over 50 years.

For a long time it was believed that cyclic stable nitroxide radicals (piperidine, pyrroline, and imidazoline >NO^•) inhibit oxidation of hydrocarbons (RH) and 1- and 1,1- ethylene substituted monomers (M) only via reaction with substrate’s alkyl radicals in accordance with Scheme 1 (Buchachenko, 1965; Denisov & Afanas'ev, 2005; Mogilevich & Pliss, 1990). If substrate is M then chains are propagated by polyperoxide radicals (MO₂^•) through its addition to monomer’s double bond in accordance with the reaction: MO₂^• + M → M^• (Mogilevich & Pliss, 1990).

Scheme 1.

Classical mechanism of organic compounds oxidation inhibited by nitroxide radicals

At the same time a probability of direct reaction of nitroxide with peroxide radicals is considered in a number of works (Barton, 1998; Goldstein & Samuni, 2007; Offer & Samuni, 2002; Pliss et al., 2010a, 2010b, 2012). Therefore it is necessary to review the most significant results in the field of kinetics and mechanism of elementary reactions of piperidine, pyrroline, and imidazoline >NO^• with active particles of chemical and biochemical oxidation processes. Such an attempt has been made in this review.

Structures of nitroxide radicals and corresponding hydroxylamines which reactions’ mechanisms were analyzed in this work are presented in Figure 1.

Figure 1.

Structures of nitroxide radicals and corresponding hydroxylamines

2. Classical mechanism of organic compounds liquid phase oxidation inhibited by stable nitroxide radicals

For the first time Scheme 1 was proposed by A. Buchachenko with staff to describe the oxidation of ethylbenzene in presence of >NO^• (II) and (III) (Buchachenko, 1965). k₄/k₁ Values (Table 1) were obtained from kinetic data of some organic compounds’ initiated oxidation in presence of >NO^•. It can be seen that nitroxide radicals inhibit oxidation of methacrylic and acrylic ethers more effectively rather than oxidation of alkylaromatic compounds: k₄/k₁ values on average an order of magnitude greater for methacrylates and acrylates as compared with styrene, benzene, and cumene (Table 1).

At the same time k₄/k₁ value for methyl methacrylate (0.36) is close to that for cyclohexyl methyl ether (0.33) (Kovtun et al., 1974). Such results prove an important role of polar effects in reactions of >NO^• with alkyl radicals during vinyl monomers oxidation.

So it should be noted that inhibiting activity of >NO^• increases along with length of methacrylic ethers’ alkyl substitute: k₄/k₁ value increases more than 3 times from methyl ether to ionylic ether. The similar trend also takes place for acrylic ethers (Table 1).

M^• (R^•)	k4/k1 Value		Reference
"/>NO^• (I)	"/>NO^• (II)
~CH2C^•HC6H5; ~CH2C^•(CH3)COOCH3; ~CH2C^•(CH3)COO–n-C4H9; ~CH2C^•(CH3)COO–iso-C4H9; ~CH2C^•(CH3)COO–n-C9H19; ~CH2C^•HCOOCH3; ~CH2C^•HCOO–n-C4H9; CH3C^•HC6H5; (CH3)2C^•C6H5	—; 0.36; 0.72; 0.72; 1.20; 2.27; 5.20; 0.04; 0.05	0.10; 0.37; 0.72; 0.72; 1.20; 2.27; 5.20; —; —	(Browlie & Ingold, 1967); (Pliss & Aleksandrov, 1977); (Pliss & Aleksandrov, 1977); (Pliss & Aleksandrov, 1977); (Pliss & Aleksandrov, 1977); (Pliss & Aleksandrov, 1977); (Pliss & Aleksandrov, 1977); (Browlie & Ingold, 1967); (Kovtun et al., 1974)

Table 1.

k₄/k₁ Values in oxidizing monomers and hydrocarbons at 323 K

Absolute k₄ values were measured in (Aleksandrov et al., 1979) by ESR spectroscopy method (Table 2). We note that >NO^• is one of the strongest acceptors for alkyl radicals. k₄ Values are close to ones for molecular oxygen addition to alkyl radicals (k₁ ≥ 1∙10⁷ M^–1∙s^–1 (Aleksandrov et al., 1979)). k₄ Values for reactions of >NO^• (I) – (VII) with alkyl radicals of methyl methacrylate at 323 K are within a limits of (0.8 – 2.0)∙10⁷ M^–1∙s^–1 (Table 2). Even higher k₄ values for the reaction of >NO^• (I) with R^• of low molecular weight at 291 K were obtained in (Bowry & Ingold, 1992) by laser flash photolysis method: these values are within a limits of 1∙10⁶ – 2∙10⁹ M^–1∙s^–1.

The probability of >NO^• participation in chain initiation process via its reaction with monomer’s π-bond was estimated in (Ruban et al., 1967) using the reaction of >NO^• (I) and (III) with styrene and α-methyl styrene as example. Reaction

>NO^• + CH₂=C(X)C₆H₅ → >NO–CH₂–C^•(X)C₆H₅ (where X = H or CH₃)

at 393 K proceeds with constant rate value which equals to 4.6 M^–1∙s^–1 in styrene, but in α-methyl styrene this reaction doesn’t proceed at all even at 453 K (Ruban et al., 1967). It’s clear that >NO^• initiating function completely suppresses by its participation in reaction (4).

Further we will see that reaction (4) is not the only one in oxidation inhibition by nitroxide radicals.

M^•	"/>NO^•	k4, M^–1∙s^–1
~CH2C^•HC6H5; ~CH2C^•(CH3)COOCH3; ~CH2C^•(CH3)COOCH3; ~CH2C^•(CH3)COOCH3; ~CH2C^•(CH3)COOCH3; ~CH2C^•(CH3)COOCH3; ~CH2C^•(CH3)COOCH3; ~CH2C^•(CH3)COOCH3; ~CH2C^•(CH3)COO–n-C4H9; ~CH2C^•(CH3)COO–iso-C4H9; ~CH2C^•HCOOCH3; ~CH2C^•HCOO–iso-C4H9; cyclo-C^•6H11; (CH3)2C•CN (in benzene)	I; I; II; III; V; VI; VII; VIII; I; I; I; I; I; I	8.0∙10^6; 1.2∙10^7; 0.8∙10^7; 0.8∙10^7; 1.4∙10^7; 1.6∙10^7; 1.2∙10^7; 2.0∙10^7; 1.2∙10^7; 0.9∙10^7; 3.0∙107; 1.8∙107; 3.0∙107; 8.6∙107

Table 2.

Rate constants for the reaction M^• (R^•) + >NO^• at 323 K (Aleksandrov et al., 1979)

3. Multiple chain-breaking by stable nitroxide radicals

It was proved on oxidation of a number of compounds that oxidation chains propagate by peroxide radicals which possess redox properties. These are HO₂^• radicals (cyclohexadiene (Howard & Ingold, 1967), 1,2-ethylene substituted and 1,4-butadiene substituted monomers (Mogilevich & Pliss, 1990)), >C(OH)O₂^• (alcohols (Kharitonov & Denisov, 1967)), and >CH–CH(OO^•)N< (aliphatic amines (Aleksandrov, 1987)). Dual reactivity of these radicals results in multiple >NO^• participation in chain termination processes (Denisov, 1996). So for hydroperoxide radical this process can be described with the following reactions (Denisov, 1996):

HO₂^• + >NO^• → >NOH + O₂(5.1)

HO₂^• + >NOH → >NO^• + H₂O₂(5.2)

Let’s perform the analysis of oxidation mechanism with >NO^• regeneration and one without it.

3.1. Analysis of oxidation mechanism without nitroxide radical regeneration

In accordance with Scheme 1 initial rate process (W) without >NO^• regeneration would be described by the following equation (W = W₀ when [>NO^•]₀ = 0):

$$W_i\left(\frac{W_0}{W}-\frac{W}{W_0}\right)=\frac{k_4{[{\text{>NO}}^{\text{•}}]}_0{W}_0}{k_1[{\text{O}}_{\text{2}}]}$$E1

If k₄[>NO^•]₀ >> k₃[RO₂^•] then

$$W=\frac{k_1[{\text{O}}_{\text{2}}]}{k_4{[{\text{>NO}}^{•}]}_0}{W}_i$$E2

So the rate process in linear termination mode (high [>NO^•]₀) is directly proportional to the partial oxygen pressure (Po₂). Therefore if oxygen is substituted by air the oxidation rate is to decrease 5 times. Such results were gained in (Browlie & Ingold, 1967; Pliss & Aleksandrov, 1977). But here is one important circumstance. From literature data (Aleksandrov, 1987) it’s known that the reduction of nitroxide to corresponding hydroxylamine (>NOH) occurs via the reaction of aminoalkyl radical >N–C^•H–CH< with nitroxide radical as >NO^• attack to β-C–H bond of alkyl radical.

>N–C^•H–CH< + NO^• → >NOH + >N–CH=C<

The hydroxylamines being formed are thermally stable under experimental conditions (Aleksandrov, 1987). If we assume that >NOH is able to react with R^•

>N–C^•H–CH< + >NOH → >N–CH₂–CH< + >NO^•,

then >NO^• stoichiometric coefficient must be more than 1.

Let’s consider the probability of >NO^• cross-dispropotionation with other alkyl radicals. Such a consideration is quite useful cause at physiological Po₂ values in body tissues of higher animals and humans (5 – 50 torus) oxygen concentration is less than 1∙10^–4 M (Porter & Wujek, 1984). In this case inequality [RO₂^•] >> [R^•] is not satisfied and it’s necessary to take into account alkyl radicals’ participation contribution. This can be done by modifying Scheme 1 for vinyl monomers’ oxidation (Scheme 2).

Scheme 2.

Mechanism of organic compounds oxidation inhibited by nitroxide radicals taking into account M^• with >NO^• disproportionation

Let’s estimate >NO^• recombination and disproportionation shares ratio according to reactions (4.1) and (4.2). There’s almost no any experimental data for such estimation, so we have to use the results of quantum-chemical calculations.

Table 3 represents the values of quantum energies of >NO^• reactions

In chemical thermodynamics quantum-chemically calculated reaction energy is used. It is a difference between full energies of reaction’s products and reagents. This value often correlates with experimental value – enthalpy of reaction (http://cccbdb.nist.gov/).

with peroxyalkyl radicals ~OOM^• (DFT B3LYP/6-31G* calculation similar to one in (Becke, 1993)). As a structural unit we’ve used –OOCH₃ fragment. As can be seen from the table, such operation is quite acceptable: substitution of –OOCH₃ to –CH₂CH₃ or to –CH₂CH₂CH₃ doesn’t result in significant changes in energy values calculated.

It should be noted that in accordance with calculated results recombination’s probability is significantly greater as compared with disproportionation’s one: mean difference in energies is greater or equal of 30 kJ/mol. However, cross-disproportionation in liquid phase also can not be excluded: polar effects may have a significant effect especially if there are polar groups in conjugation with β-C–H bond (Roginskii, 1987). Recombination and disproportionation energies lowering during methyl group addition to α-position of radical center ~OOM^• also seem to be a logical cause as a steric effects appear in this case.

M^•	Reaction type
M^•+ "/>NO^• → MON<	M^• + "/>NO^• → M–H + "/>NOH
C6H5CH^•CH2OOCH3	–121	–77
C6H5CH^•CH2CH3	–136	–69
C6H5CH^•CH2CH2CH3	–125	–70
C6H5C^•(CH3)CH2OOCH3	–79	–70
C6H5C^•(CH3)CH2CH3	–94	–68
C6H5C^•(CH3)CH2CH2CH3	–69	–67
CH3OC(=O)CH^•CH2OOCH3	–127	–111
CH3OC(=O)CH^•CH2CH3	–172	–145
CH3OC(=O)CH^•CH2CH2CH3	–144	–93
CH3OC(=O)C^•(CH3)CH2OOCH3	–79	–61
CH3OC(=O)C^•(CH3)CH2CH3	–93	–75
CH3OC(=O)C^•(CH3)CH2CH2CH3	–88	–79
Mean value	–111	–82

Table 3.

Reaction energies of alkyl radicals with >NO^• (I) (kJ/mol)

Reactions (4.2) and (4.3) rates ratio can be estimated on the basis of experimental kinetic data of >NO^• (I) consumption in cumene, styrene, or methyl methacrylate in inert atmosphere. Experiment conditions: 323 K, atmosphere of argon, [>NO^• (I)]₀ = 5∙10^–3 M, initiator – azobisisobutyronitrile, W_i = 1∙10^–7 M∙s^–1. The dynamic equilibrium is to set over time in case of reactions (4.2) and (4.3) and observed residual ESR signal value is to increase along with [>NO^•]₀ growth since the following equalities are valid during that equilibrium:

$$k_{4.2}[{\text{R}}^{\text{•}}][\overline{>{\text{NO}}^{•}}]=k_{4.3}[{\text{R}}^{\text{•}}][\overline{>\text{NOH}}]$$E3

$$[\overline{>\text{NOH}}]={[>{\text{NO}}^{•}]}_0-[\overline{>{\text{NO}}^{•}}]$$E4

$$[\overline{>{\text{NO}}^{•}}]=\frac{k_{4.3}{[>{\text{NO}}^{•}]}_0}{k_{4.2}+k_{4.3}}$$, whence

$$\frac{k_{4.2}}{k_{4.3}}=\frac{{[>{\text{NO}}^{•}]}_0}{[\overline{>{\text{NO}}^{•}}]}-1$$E5

After completely >NO^• consumption the residual ESR signal amplitude doesn’t exceed a noise level under experimental conditions. This corresponds to potential stationary >NO^• concentration of less than 10^–7 M (ESR spectrometer Adani CMS 8400). In this case [>NOH] ≈ [>NO^•]₀ and at [>NO^•]₀ = 5∙10^–4 M we have the following value of k_4.2/k_4.3 ratio:

k_4.2/k_4.3 = (5∙10^–4/1∙10^–7) – 1 ≈ 5∙10⁴

And now the ratio of (4.3) to (4.2) reaction rates can be estimated:

$$\frac{W_{4.3}}{W_{4.2}}=\frac{k_{4.3}[\overline{>\text{NOH}}]}{k_{4.2}[\overline{>{\text{NO}}^{•}}]}\approx 2\cdot {10}^{-5}\frac{[\overline{>\text{NOH}}]}{[\overline{>{\text{NO}}^{•}}]}$$E6

.

Therefore in range of up to 99% of >NO^• consumption reaction’s (4.3) share is less than 1% of reaction (4.2), so practically there’s no any >NO^• regeneration at all. That is f = 1 in inert atmosphere and in these substrates’ medium. It’s obvious that reaction (4.2) would be completely suppressed by reaction of >NOH with RO₂^• at [O₂] > 1∙10^–4 M.

3.2. Analysis of oxidation mechanism with nitroxide radical regeneration

In case of >NO^• regeneration the oxidation’s mechanism describes by Scheme 3.

Scheme 3.

Mechanism of organic compounds oxidation inhibited by nitroxide radicals taking into account >NO^• regeneration

The following equation is valid for this scheme:

$$W_i\left(\frac{W_0}{W}-\frac{W}{W_0}\right)=\frac{k_4{[{\text{>NO}}^{\text{•}}]}_0{W}_0}{k_1[{\text{O}}_{\text{2}}]}+\frac{2k_5{[{\text{>NO}}^{\text{•}}]}_0{W}_i^{0.5}}{k_3^{0.5}}$$E7

where k₅ = (k_5.1[>NO^•] + k_5.2[>NOH])/2[>NO^•]₀.

Kinetic analysis shows that at [O₂] ~ 1∙10^–2 M and [>NO^•]₀ < 10^–4 M the contribution of reaction (4) to chain termination process is negligible, and then

$$\frac{W_0}{W}-\frac{W}{W_0}=\frac{2k_5{[{\text{>NO}}^{•}]}_0}{{\left(W_i{k}_3\right)}^{0.5}}$$E8

With the drop of Po₂ and small share of quadratic chain termination the oxidation rate will decrease not linearly, but slower. Such facts were found for instance in (Pliss & Aleksandrov, 1977; Ruban et al., 1967).

Reaction (5.1) proceeds as disproportionation of nitroxide and peroxide radicals (Denisov, 1996):

HO₂^• + >NO^• → >NOH + O₂

>C(OH)O₂^• + >NO^• → >NOH + >C=O +O₂

>CH–CH(OO^•)N< + >NO^• → >NOH + >C=CH–N< + O₂

>NO^• regeneration and multiple chain termination processes are caused just by subsequent reaction (5.2). Measured kinetic inhibiting factors

Inhibiting factor is ratio of real induction period (t) to theoretical period of inhibitor conversion ((), i.e. finh = t/(, where ( = f[>NO•]/Wi (f – stoichiometric inhibiting factor).

for different nitroxide radicals and substrates presented for example in review (Denisov, 1996). The most of f values greater than ten and reflects just a lower bound of this value.

4. Specific features of nitroxide and peroxide radicals reactions in biological systems and in liquid phase organic substrates

Like transition metals, nitroxide radicals can easily transform both to oxidized (oxoammonium cation) and to reduced (hydroxylamine) forms (Berliner, 1998; Sen' & Golubev, 2009; Zhdanov, 1992). This fact, along with >NO^• ability to penetrate through cell membranes and with its paramagnetic properties, suggests that nitroxide radicals poses a number of unique features unlike the compounds of any other class. Like antioxidants and mimetics of superoxide dismutase enzyme, >NO^• are able to supply an effective protection for cells and tissues (Denisov & Afanas'ev, 2005; Soule et al., 2007; Wilcox, 2010). Nitroxide radicals inhibit oxidation of lipids in fatty acids’ micelles (Damiani et al., 2002; Noguchi et al., 1999), liposome membranes (Damiani et al., 2002; Wilcox, 2010), lipoproteins (Damiani et al., 1994), and in low density microsomes (Antosiewicz et al., 1995; Nilsson et al., 1990). At the moment there’s not enough information concerning >NO^• reactions with redox peroxide radicals to understand such reactions’ mechanisms. In fact, there is no any certain agreement on this reaction, so some authors consider it as unlikely one (Blough, 1988; Browlie & Ingold, 1967; Damiani et al., 2002; Denisov, 1996).

Our recent results concerning reactions of >NO^•(I) – (VII) with MO₂^• radicals of 1,1- substituted ethylenes allows suggestion that such reaction’s probability is quite high.

Let’s review some experimental data in this field to understand the situation.

4.1. Nitroxide and peroxide radicals reaction under conditions modeling biological systems

Barton et al. assumed that in reaction of >NO^• (I) with (CH₃)₃COO^• the formation of quite stable intermediate should take place (Barton et al., 1998):

>NO^• + (CH₃)₃COO^• → (CH₃)₃COOON<

Further this intermediate should decompose to a number of products with concomitant formation of molecular oxygen and >NO^• regeneration according to the following very speculative scheme (Scheme 4) with no any kinetic evidence (Barton et al., 1998).

Scheme 4.

Mechanism of nitroxide with tert-butyl peroxide radicals reaction according to (Barton et al, 1998)

Stipa attempted to prove this scheme with ab initio quantum-chemical calculations (Stipa, 2001). The calculations were performed using Gaussian 98 Hartree-Fock method and complete basis set CBS-QB3. H₂NO^• Radical was used as a model of >NO^• (I) in view of available computer resources limitations (work was submitted in April 2001). The calculations’ results indicate the possibility of Scheme 4.

This conclusion seems to be quite controversial since radical H₂NO^• can not provide an adequate >NO^• (I) model. For example, standard enthalpy calculated for the first reaction stage was –1.794 kcal/mol (tabelle 2 in (Stipa, 2001)), i.e. this value is not very different from zero within the quantum-chemical calculations accuracy. This suggests that the studied trioxide apparently must be thermodynamically unstable structure. At the same time, radical H₂NO^• is much more active than simulated >NO^• (I). It’s easy to show with Density Functional Theory (DFT) calculations (Becke, 1993). Quantum energy values of radicals H₂NO^• and >NO^• (I) recombination with CH₃O^• and CH₃OO^• were calculated by DFT B3LYP/6-31G* (similar calculation is shown in Table 3). The results are shown below.

Radical	Recombination energy, kJ/mol
"/>NO^•(I)	H2NO^•
HO^•	–28.3	–98.4
HOO^•	48.1	–20.4
CH3^•	–150.6	–232.8
CH3O•	11.5	–58.2
CH3OO•	60.3	9.92

Table 4.

Even this simple example shows that stable nitroxide radical >NO^• (I) is significantly less active than H₂NO^•.

Offer and Samuni also suggest that stable trioxide formation proceeds in reaction of tert-amidinopropyl radicals with >NO^• (I) and (III) in phosphate buffer at pH 7.4 and 310 K (Offer & Samuni, 2002):

(H₂N)₂⁺CC(CH₃)OO^• + >NO^• → (H₂N)₂⁺CC(CH₃)OOON<

This reaction was studied with combination of ESR-spectroscopy method and cyclic voltammetry, but no any kinetic evidences of product formation and its subsequent transformation were provided.

Brede et al. studied the reaction of n-C₁₇N₃₅OO^• with >NO^• (I) with pulse radiolysis at room temperature (Brede et al., 1998). The rate constant value k < 10⁵ M^–1∙s^–1 was specified but the reaction’s mechanism wasn’t discussed.

Goldstein S. and Samuni also determined the rate constants of reactions of CH₃OO^•, (CH₃)₃COO^•, CH₂(OH)OO^•, and HO₂^• with >NO^• (I) – (IV), (X) – (XII) with pulse radiolysis at room temperature (Goldstein & Samuni, 2007). The values obtained are shown in Table 4. The mechanism of RO₂^• + >NO^• reaction was discussed; therefore let’s consider this paper in more detail.

It was shown that nitroxide with peroxide radicals’ reaction mainly results in formation of corresponding oxoammonium cations. In case of (CH₃)₃COO^• the formation of stable cation radical >NO^• (I) and decay products of relatively unstable cation radical >NO^• (II) was spectrophotometrically detected. In case of HOO^• the reaction with piperidine nitroxide radicals is catalyzed by anion H₂PO₄^– as noted in (Goldstein & Samuni, 2007). Therefore under physiological conditions (pH 7.4 and 5∙10^–2 M phosphate) observed rate constants for piperidine nitroxide radicals are slightly greater than those shown in Table 4. Moreover, catalysis by H₂PO₄^– anions implies that nitroxide with peroxide radicals’ reaction proceeds according to inner-sphere electron transfer mechanism when >NOOOR adduct’s decomposition can undergo general acid catalysis:

$$>{\text{NO}}^{•}+{\text{ ROO}}^{•}\stackrel{}{\rightleftarrows }>\text{NOOOR}$$E9

$$>\text{NOOOR }\stackrel{}{\rightleftarrows }>{\text{N}}^{+}=\text{O }+{\text{ ROO}}^{–}$$E10

$$>\text{NOOOR }+{\text{ H}}_{\text{2}}{\text{PO}}_{\text{4}}{}^{–}\stackrel{}{\rightleftarrows }>{\text{N}}^{+}=\text{O }+\text{ ROOH }+{\text{ HPO}}_{\text{4}}{}^{\text{2}–}$$E11

It’s obvious that in absence of catalysis the adduct’s formation may also occur, but inner-sphere electron transfer mechanism still can not be excluded:

$$>{\text{NO}}^{•}+{\text{ ROO}}^{•}\stackrel{}{\rightleftarrows }>{\text{N}}^{+}=\text{O }+{\text{ ROO}}^{–}$$E12

Known rate constants of reaction HO₂^• (>C(OH)O₂^•) + >NO^• (I) and (III) in organic solvents are in the range of 1.1∙10⁴ – 2.1∙10⁵ M^–1∙s^–1 at 323 K (Aleksandrov, 1987; Wilcox, 2010), which is two-three orders of magnitude lower than values shown in Table 5. Such a huge difference may hardly be explained only by the reaction’s specificity in phosphate buffer. Further reaction of radicals HO₂^• and CH₂(OH)OO^• with >NO^• proceeds, as is well known, as disproportionation rather than recombination (Denisov, 1996; Denisov & Afanas'ev, 2005; Mogilevich & Pliss, 1990).

"/>NO^•	CH3OO^•	(CH3)3COO^•	CH2(OH)OO^•	^*) HO2^•
I	2.8∙10^7	5.1∙10^7	1.0∙10^8	1.1∙10^8
II	2.8∙10^5	5.4∙10^5	—	<6∙10^6
III	3.3∙10^6	5.4∙10^6	4.4∙10^7	2.7∙10^7
IV	1.0∙10^6	1.5∙10^6	—	<1∙10^7
X	8.1∙10^5	1.1∙10^5	9.0∙10^6	1.1∙10^6
XI	9.6∙10^5	1.5∙10^6	—	1.1∙10^6
XII	5.0∙10^4	6.7∙10^4	—	1.6∙10^5

Table 5.

Rate constants (M^–1∙s^–1) of ROO^• + >NO^• reaction (Goldstein & Samuni, 2007).

It’s important that authors (Goldstein & Samuni, 2007) on the base of experimental data suggested that rate constant of reaction RO₂^• + >NOH doesn’t exceed 1∙10⁵ M^–1∙s^–1, i.e. this reaction is much slower as compared with RO₂^• + >NO^• (Table 4). Thereby we note that, as it well known (Denisov, 1996; Denisov & Afanas'ev, 2005; Mogilevich & Pliss, 1990), upon a competition of reactions (5.1) and (5.2) (see Scheme 2) the rate-limiting reaction is just the first one.

As can be seen from the results above, the mechanism of nitroxide with peroxide radicals’ reactions in biological systems isn’t elucidated at all. The authors of works analyzed are inclined to possibility of >NO^• reaction not only with peroxide radicals poses redox properties: HO₂^•, >C(OH)O₂^•, but with RO₂^• which are oxidants only: (CH₃)₃COO^•, n-C₁₇H₃₅OO^• (Barton et al., 1998; Brede et al., 1998; Goldstein et al., 2003; Goldstein & Samuni, 2007; Offer & Samuni, 2002 ; Stipa, 2001). It is assumed that such a reaction occurs as recombination with formation of trioxide. According to the authors of papers cited, nitroxide radicals are able to provide protection against oxidation at extremely low concentrations due to the regeneration process resulting from the reaction of corresponding oxoammonium cations with common biological reducing agents.

Hereby it’s interesting to consider the reaction of >NO^• with RO₂^• which are only oxidants under conditions when oxoammonium cations’ formation is improbable, i.e. during an oxidation in organic phase.

4.2. Nitroxide radicals reactions with peroxide radicals of 1- and 1,1- ethylene substituted monomers

As it has already been mentioned above, reactions of >NO^• with peroxide radicals of 1- and 1,1- ethylene substituted monomers were discovered recently (Pliss et al., 2010a, 2010b, 2012). Authors (Pliss et al., 2010a, 2010b) on the basis of kinetic data of styrene’s and (meth)acrylates’ oxidation in presence of piperidine, pyrroline, and imidazoline >NO^• suggested that nitroxide radicals inhibit the oxidation process via >NO^• reaction with substrate’s both alkyl and peroxide radicals, and moreover >NO^• regeneration occurs during chain termination process in accordance with reactions:

MO₂^• + >NO^• → product + >NOH(5.1)

MO₂^• + >NOH → MOOH + >NO^•(5.2)

The following results served grounds for these assumptions: oxygen consumes linearly in presence of >NO^• for all monomers for a long period of time. That period is greater than the theoretical induction period, and if Po₂ reduces to five times (from 1∙10⁵ to 0.2∙10⁵ Pa) the oxidation rate decreases to less than two times (Pliss et al., 2010a, 2010b). But of course it is unacceptable to make any definite conclusions about detailed mechanism just on the basis of the oxygen consumption kinetic data only.

In (Pliss et al., 2012) >NO^• antioxidant activity was studied during styrene’s oxidation using a complex of kinetic methods in combination with quantum-chemical calculations and kinetic modeling. The choice of styrene is caused by the following circumstances. Firstly, the reaction of styrene’s inhibited oxidation is not complicated by complexation process as it is in case of many other vinyl compounds (acrylic monomers for example). Secondly, high reactivity of styrene’s double bond makes it possible to study this process under long chains conditions even if oxidation is quite strongly inhibited. Thirdly, in case of styrene the rate constants of elementary stages are known for many key reactions, and this knowledge makes kinetic modeling significantly easer to carry out.

Let’s consider the results of this work and some of our new data.

Oxidation kinetics was studied in area of initial O₂ consumption rates in temperature range of 310 – 343 K with highly sensitive capillary microvolumometer according to technique (Loshadkin et al., 2002). Initial >NO^• concentrations were in range of 10^–7 – 10^–3 M. Experiments were carried out at Po₂ = 20 or 100 kPa. In special cases oxygen-argon mixes were prepared to obtain the oxidation rates dependences on [O₂]. Initiation rate W_i was determined with inhibition method by detection of induction period ending time τ_ind and application of known equation W_i = 2[InH]₀/τ_ind. 6-Hydroxy-2,2,5,7,8-pentamethylbenzochroman was used as inhibitor (InH). Kinetic modeling was performed as described in (Loshadkin et al., 2002).

Values of styrene’s oxidation rates inhibited by different >NO^• under oxygen and air saturation conditions and when quadratic termination share is no more than 25% are presented in Table 6. As seen from the table, the oxidation’s rate for different >NO^• from oxygen to air decreases substantially less than five times. This fact according to (Aleksandrov, 1987; Denisov & Afanas'ev, 2005; Kharitonov & Denisov, 1967; Kovtun et al., 1974; Mogilevich & Pliss, 1990; Pliss & Aleksandrov, 1977; Denisov, 1996) suggests that nitroxide radicals react with both M^• and MO₂^•.

Kinetics of >NO^•(III) consumption at its different initial concentrations are presented in Figure 2. From this data it follows that according to inhibition by reaction (4) >NO^• should consume much faster than it happens in fact. With special experiments it was shown that value of inhibiting factor e.g. for >NO^• (III) and >NO^• (IV) is more than 7 (Pliss et al., 2012), so it suggests that >NO^• regeneration process occurs upon chain termination. We note that this effect doesn’t depend on styrene’s concentration.

["/>NO^•]0∙10^5, M	W∙106, M∙s–1		Wo2 / Wair
Po2 = 1∙10^5 Pa (oxygen)	Po2 = 0.2∙10^5 Pa (air)
0	11.0	11.0	1.00
"/>NO^•(I)
2.8	4.75	2.58	1.84
4.1	4.37	2.84	1.54
"/>NO^•(II)
4.2	3.76	2.12	1.78
14	2.88	1.17	2.45
"/>NO^•(III)
5.7	4.34	2.19	1.98
18	3.13	1.30	2.40
"/>NO^•(IV)
4.0	5.67	4.09	1.38
8.0	5.07	2.20	2.30
"/>NO^•(V)
5.9	4.90	3.21	1.53
17	2.38	0.78	3.06

Table 6.

Kinetic parameters of styrene’s oxidation inhibited with >NO^•; W_i = 1.0∙10^–8 M∙s^–1 (Pliss et al., 2012)

Figure 2.

Kinetics of >NO^• (III) consumption during styrene oxidation (in relative coordinates); points: experimental data, curves: a result of simulation. Po₂ = 20 kPa; W_i = 1.0∙10^–8 M∙s^–1; [>NO^•]₀, M: 1 – 2.3∙10^–6, 2 – 5.9∙10^–6, 3 – 1.2∙10^–5, 4 – 2.8∙10^–5 (Pliss et al., 2012).

Styrene’s oxidation can be effectively inhibited by hydroxylamines. This assertion confirms with distinct induction period on oxygen consumption’s kinetic curve (typical one represented at Figure 3 (Pliss et al., 2012)). Rate constants of such antioxidants’ reactions with peroxide radicals can be determined from inhibited oxidation’s rate dependence on time according to the following equation (Loshadkin et al., 2002):

$$F=\ln \frac{1+W/W_0}{1-W/W_0}-\frac{W_0}{W}=\frac{k_{5.2}{W}_0}{k_2[\text{M}]}t+const$$E13

But the problem is that oxidation rate remains significantly lower than W₀ after the inhibiting period (see Figure 3) since >NO^• being formed is an inhibitor of oxidation itself. However the kinetic modeling shows that in this case in equation (5) we can substitute W₀ value to the value of oxidation’s rate at after-induction period. Herewith k_5.2 determination error is less than 10%. Calculated k_5.2 mean value at 323 K for >NOH (III), equal to 4∙10⁶ M^–1∙s^–1 (Pliss et al., 2012), was later used in mechanism’s kinetic modeling.

Dependences of >NO^• consumption and its accumulation from corresponding >NOH on time during styrene’s oxidation at Po₂ = 20 kPa presented at Fig. 4 (ESR-spectroscopy method). It’s seen that hydroxylamine being injected quickly transforms to >NO^• and its maximum concentration differs from [>NO^•]₀ by less than 10%. It’s important that hereafter consumption rates of injected >NO^• and one being formed from hydroxylamine are almost the same (see curves 1 and 2 at Fig. 4).

As already been mentioned (see Section 3), if chains propagates by HO₂^•, >C(OH)O₂^•, or >CH–CH(OO^•)N< radicals then inhibition proceeds as disproportionation of these radicals with >NO^•. Herewith hydroxylamine being injected quickly transforms to >NO^• which almost doesn’t consume but effectively inhibits an oxidation of corresponding substrates. So in this case the inhibiting factor values are more than 100 (Kovtun et al., 1974). Therefore it should be considered that in case of styrene’s oxidation the way of irreversible >NO^• consumption is reaction (4).

Figure 3.

Kinetics of O₂ consumption during styrene’s oxidation: 1 – without inhibitor; 2 – [>NOH (III)] = 2∙10^–5 M; 3 – anamorphous of curve 2 in coordinates of equation (5); Po₂ = 20 kPa; W_i = 1.0∙10^–8 M∙s^–1 (Pliss et al., 2012)

Figure 4.

Kinetics of >NO^• (III) consumption (1) and its accumulation from corresponding hydroxylamine (2) during styrene’s oxidation: dots – experimental data, curves – modeling results; [>NO^• (III)]₀ = [>NOH (III)]₀ = 2.9∙10^–5 M; Po₂ = 20 kPa; W_i = 1∙10^–8 M∙s^–1 (Pliss et al., 2012)

As it was mentioned above (see section 3.1), reaction (4) may proceed both as recombination and as disproportionation. Target experiment’s results presented at Figure 5. Rate of >NO^• (III) consumption in styrene (atmosphere of argon) during initiated oxidation was equal to initiation rate, and this >NO^• consumption was proceeded up to detection limit of ESR-spectrometer (≤ 1∙10^–7 M). After that argon was substituted to oxygen and, as can be seen at Figure 5, >NO^• signal was appeared again.

These cycles were repeatedly detected several times until we reached the spectrometer’s detection limit. Each time >NO^• was recrudesced in share about 25–30% of its initial concentration. This fact confirms the assumption that reaction (4) also may proceed as disproportionation due to β-C–H bond of styrene’s alkyl radical (~CH₂C^•HC₆H₅) with olefin’s formation ~CH=CHC₆H₅ (M_–H):

M^• + >NO^• …→ >NOR(4.1)

M^• + >NO^• …→ M_–H + >NOH(4.2)

Thus >NO^• signal may appear due to the reaction (5.2) upon oxygen blow (see Scheme 5 below).

Figure 5.

Kinetics of >NO^• (III) consumption in styrene: [>NO^• (III)]₀ = 2.8∙10^–5 M; W_i = 1∙10^–8 M∙s^–1 (Pliss et al., 2012)

Another one probable reason of this effect (Figure 5) is reaction MO₂^• + >NOR → product + >NO^• (5.3) that was first proposed in (Denisov, 1982). As >NO^• regeneration source, this reaction was studied in detail for reactions of some alkoxyamines >NO^• (I) with peroxide radicals of cumene and cyclohexylmethyl ether at 338 K (Kovtun et al., 1974). Obtained k_5.3 values (1 – 26 M^–1∙s^–1) suggest that >NOR being studied in (Kovtun et al., 1974) are weak inhibitors. This conclusion also is confirmed with the dependences of styrene’s oxidation rates on >NOR (I) and >NO^• (III) concentrations (Pliss et al., 2012).

All of the experimental data and our previous results (Pliss et al., 2010a, 2010b, 2012) allow us to provide the following formal kinetic scheme of styrene’s oxidation inhibited by aliphatic stable nitroxide radicals:

Scheme 5.

Detailed mechanism of vinyl monomers oxidation inhibited by nitroxide radicals

We’ve used this scheme for kinetic modeling (Pliss et al., 2012). Values of k₁ – k_4.1, k_4.3, k_5.3 (M^–1∙s^–1) were taken from the literature and values of k_4.2 and k_5.1 were obtained from modeling. Figures 2 and 4 shows that calculated curves are of satisfactorily consistent with experimental data. This indirectly confirms the reliability of Scheme 5.

Kinetic analysis shows that [M^•] << [MO₂^•] when [O₂] ~ 1∙10^–2 M. In this case reactions (3.1), (3.2), (4.2), (4.3), and (5.3) can be neglected. Then the scheme including reactions (i), (1), (2), (3.3), (4.1), (5.1), and (5.2) can be described by equation:

$$W_i\left(\frac{W_0}{W}-\frac{W}{W_0}\right)=\frac{k_4{[{\text{>NO}}^{\text{•}}]}_0{W}_0}{k_1[{\text{O}}_{\text{2}}]}+\frac{2k_5{[{\text{>NO}}^{\text{•}}]}_0{W}_i^{0.5}}{k_{3.3}^{0.5}}$$E14

,

where k₅ = (k_5.1[>NO^•] + k_5.2[>NOH])/2[>NO^•]₀. If [>NO^•] < 10^–4 M then chain termination by reaction (4) can be neglected, therefore that scheme can be described by equation:

$$\frac{W_0}{W}-\frac{W}{W_0}=\frac{2k_5{[{\text{>NO}}^{•}]}_0}{{\left(W_i{k}_{3.3}\right)}^{0.5}}$$E15

.

Previously (Pliss et al., 2010a, 2010b) we’ve analyzed a simplified scheme including reaction (i), (1), (2), (3.3), (5.1), and (5.2). We’ve calculated the values of k₅ = (5 ± 3)∙10⁴ M^–1∙s^–1 for >NO^• (I) – (V) in oxidizing vinyl monomers at 323 K and Po₂ = 1∙10⁵ Pa. These values are close enough to estimated in this present work value k_5.1 = 2.5∙10⁴ M^–1∙s^–1.

A fundamental question about the detailed mechanism of the reaction (5.1) remains open. By analogy with the oxidation of 1,2-substituted ethylenes and 1,4-substituted butadienes (Mogilevich & Pliss, 1990) we can assume that hydroxylamine’s formation is facilitated by conjugation of β-C–H bond with peroxide bridge of styrene’s polyperoxide radical:

~OO–CH₂–CH(C₆H₅)–OO^• + >NO^• → ~OO–CH₂=CH–C₆H₅ + >NOH + O₂

Peroxide bridge is an important structural unit of ~MO₂^• radical. It alters the reaction center’s electronic characteristics and increases the electrostatic term’s contribution to the transition state’s total energy (Denisov, 1996; Denisov & Afanas'ev, 2005; Mogilevich & Pliss, 1990). Probable reason of this effect is the difference in the triplet repulsion, which is close to zero in transition state of disproportionation reaction of MO₂^• with >NO^• and is sufficiently large for the reaction of >NO^• with nonconjugated C–H bond of hydrocarbon (Denisov, 1996). The latter probably explains the fact that aliphatic nitroxide radicals inhibit the hydrocarbon’s oxidation via reaction with alkyl radicals only.

The results obtained in the present study draws attention to the results gained for biological systems where it is assumed that reaction of aliphatic >NO^• with peroxide radicals proceeds via >NOOOR adduct formation decomposing to corresponding oxoammonium cations (Barton et al., 1998; Goldstein & Samuni, 2007; Offer & Samuni, 2002). The probability of such intermediate’s existence is also considered in quantum-chemical analysis (Hodgson & Coote, 2010; Stipa, 2001). Further regeneration of nitroxide radicals may be due to reaction of oxoammonium cations with common biological reducing agents (Goldstein & Samuni, 2007; Offer & Samuni, 2002).

Direct reaction MO₂^• + >NO^• → MOOON< that results to stable trioxide’s formation is seems quite doubtful for aliphatic >NO^• in organic phase at moderate temperatures (≤ 373 K). First, it’s easy to reject on the base of kinetic reasons cause in this case the kinetics of >NO^• consumption and stoichiometry of chain termination would have a different nature than those observed in numerous studies (Browlie & Ingold, 1967; Kovtun et al., 1974; Pliss et al., 2010a, 2010b, 2012; Pliss & Aleksandrov, 1977). Second, it’s easy to refute by direct quantum-chemical calculations (DFT B3LYP/6-31G*, Table 7). It’s easy to see that peroxide radicals’ addition to >NO^• is thermodynamically unfavorable.

Radical	H^•	HO^•	HOO^•	^•CH3	CH3O^•	CH3OO^•
Energy	–243.4	–28.3	48.1	–150.6	11.5	60.3

Table 7.

Energy of some radicals’ addition to >NO^• (I), kJ/mol

5. Conclusions

Thus, we must conclude that reaction of nitroxide with peroxide radicals plays an important role during styrene’s oxidation in presence of aliphatic stable >NO^•. This reaction proceeds probably as disproportionation and results to a partial >NO^• regeneration.

At the same time we emphasize that detailed mechanism of chemical and biological oxidation processes inhibited by stable nitroxide radicals is still far from being established. Therefore kinetic experiments on the key reactions involving nitroxide radicals and its conversion products (hydroxylamines, alkoxyamines, oxoammonium cations) in solutions of organic substrates and in biological systems must be carried out to solve this problem.

Acknowledgement

The authors gratefully acknowledge Vasily Sen’ for providing of nitroxide radicals and hydroxylamines that were applied in this work. The experimental part was carried out on equipment of the Scientific and educational center «Physical organic chemistry» and the Center for collective usage of scientific equipment for diagnostics of micro and nanostructures of Yaroslavl State Univercity. The work was financially supported by Ministry of Education and Science of the Russian Federation (contracts N. 02.740.11.0636, 29.03.2010 and N. 16.552.11.7006, 29.04.2011).