Theoretical investigations of the catalytic antioxidation mechanism of diarylamine and the coordination effects of Fe(III) and Fe atoms

Junming Wang^a, Weiguo Xue*^a, Zhuozheng Wang^b, Hao Li^b, Huiying Lv^a, Chaoliang Wei^a, Qingwei Kong† ^c, Xiaowei Xu^b, Kebin Chi^b, Dejun Shi^b, Yufeng Liu^a, Tuanle Li^a and Yi Luo*^bc
aPetroChina Lanzhou Lubricating Oil R&D Institute, Lanzhou, 730060, China. E-mail: xueweiguo_rhy@petrochina.com.cn
^bPetroChina Petrochemical Research Institute, Beijing, 102206, China. E-mail: luoyi010@petrochina.com.cn
^cSchool of Chemical Engineering, Dalian University of Technology, Dalian, 116024, China

First published on 26th July 2025

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Introduction

The auto-oxidation degradation process of lubricating oil is extremely likely to occur under service conditions because the oil can be in contact with oxygen easily, which is the major cause of the irreversible deterioration of lubricants. The auto-oxidation process is generally considered to involve the following free-radical chain reactions:^1–4

Initiation RH → R˙	(1)

Propagation R˙ + O2 → ROO˙	(2)

ROO˙ + RH → ROOH + R˙	(3)

Once a free radical R˙ is generated from a lubricant molecule RH under the effects of light or heat, it can react with oxygen rapidly and produce the corresponding peroxy radical ROO˙. The process is shown in eqn (2). ROO˙ further attacks lubricant molecules (eqn (3)), accompanied by the generation of hydroperoxide (ROOH) as the initial oxidation product; thus, a chain reaction is formed via the two reactions. The initial oxidation products may undergo further oxidation and condensation, leading to unexpected acids, esters, and lactones, which are believed to be responsible for the sludge deposits and bulk insoluble matter in used lubricating oil because of their role in increasing the viscosity of oil.^5–7 The deterioration of oil reduces lubricant functionality and decreases its service lifetime. This could contribute to the mechanical failure of moving parts and result in significant economic losses in the long run.^8,9 The auto-oxidation process can be inhibited or at least retarded by antioxidants that could break the chain reactions by two approaches: one is trapping free radicals without transforming themselves into reactive intermediates, and the other is decomposing hydroperoxide with the generation of unreactive nonradical products. These antioxidants include zinc dialkyldithiophosphate (ZDDP), cuprous dialkyldithiophosphate (CuDDP), organic molybdenum compounds (OMCs), organic sulfides, hindered phenols, and substituted aromatic amines.^10–19

Among the numerous types of antioxidants, diarylamines (Ar₂NH) are widely employed as radical-trapping antioxidants (RTA) because of their ashless performance and high efficiency at high temperatures. Especially, there have been mandated reductions in ZDDP in engine oil due to the poisoning effect of phosphorus on exhaust after-treatment catalysts, which limits both phosphorus and sulfur in the formulated passenger car engine oil.^12,20,21 These situations have caused diarylamines to receive increasingly extensive attention, and their applications are growing significantly.

It is found that Ar₂NH could donate its N–H hydrogen atom to the chain-carrying peroxyl radicals (ROO˙) to retard the oxidative degradation of lubricating oil.²² A long time ago, researchers found that each Ar₂NH molecule could trap two ROO˙ radicals, i.e., the stoichiometric factor for inhibition (f) is 2.0 at temperatures below ca. 100 °C; however, the f value increases at temperatures above ca. 100 °C.²³ Several mechanisms have been proposed to explain the inhibition process, while most of them have far-reaching significance. For example, Bolsman and co-workers^24,25 studied the effects of secondary amines on the inhibition of the oxidation process at a high temperature of 130 °C. They found that the f value could reach 40 for diphenylamine and suggested that the nitroxide radical (Ar₂NO˙) is an important intermediate catalyst. Haidasz and co-workers²⁶ also believed that the high stoichiometric factor was owing to the regeneration of the diarylamine during hexadecane autoxidation inhibited by the corresponding diarylnitroxide. The most critical progress for this intriguing chemistry phenomenon was achieved by Jensen et al.,²⁷ who investigated the inhibitory effects of 4,4′-dioctyldiphenylamine on the autoxidation of hexadecane. Their work suggested that the high stoichiometric factor observed for diarylamine antioxidants at elevated temperatures is significant owing to the regeneration of these antioxidants from alkoxylamines. The proposed mechanism for the catalytic inhibition by Ar₂NH and Ar₂NO˙ is designated as the Korcek Cycle, as depicted in Scheme 1. In this mechanism, Ar₂NH first reacts with ROO˙ to form Ar₂N˙, which then reacts with another ROO˙ to yield a nitroxide radical (Ar₂NO˙). Then, Ar₂NO˙ can be captured by carbon-centered radicals (R˙) from the substrate to generate Ar₂NOR, which produces the parent amine and ketones through thermal decomposition, resulting in the completion of the inhibition cycle.

Many radical-trapping antioxidants have been proposed in accordance with the Korcek cycle mechanism. Pratt's group investigated radical-trapping antioxidants for nearly two decades, achieving remarkable results in this period. One of their primary objectives is to enhance the efficacy of high-temperature RTA. They aim to accomplish this by incorporating heteroatoms, such as nitrogen,^28–31 oxygen,^32–34 and sulfur^33–35 or substituted alkyl chains,³⁶ into diphenylamine. These strategies establish an optimal balance between antioxidant activity and oxidative stability. Similarly, Yu and co-workers successfully developed sulfur-containing Schiff-base-bridged phenolic diphenylamines (SSPDs) that exhibit enhanced antioxidant properties at elevated temperatures using an innovative intramolecular synergy approach.³⁷ Following that, they elucidated the mechanisms behind radical trapping and the decomposition of peroxyl radicals in Schiff base diphenylamines (SDs), underscoring the multifunctional capabilities of these materials in antioxidant applications.³⁸

It is noteworthy that Pratt's group considered that the existing Korcek Cycle should be a simplified representation of the antioxidant cycle mechanism during their development of innovative methods for assessing RTA reaction activity.^39,40 Meanwhile, Coote et al.⁴¹ studied the antioxidant mechanism of dialkylamine, which could serve as a kind of light stabilizer, through high-level ab initio molecular orbital theory calculations and found that several mechanisms proposed by predecessors were unreasonable. Nevertheless, to date, the detailed mechanistic picture of the antioxidant process of diarylamines in lubricating oil remains unclear. It is also important to elucidate the oxidation inhibition mechanism for the design and application of diarylamine. Therefore, our objective is to investigate the detailed antioxidant mechanism of diarylamine after being inspired by other researchers.

In fact, metals exist extensively in oil in most practical lubricating situations, which come from equipment wear and tear or inorganic additives in operation, such as antioxidants, anticorrosives, and dispersants. The metals, such as Ag, Al, Ti, Fe, and Cu, exist in lubricating oil as soluble organometallic species or metallic particles; some of these species may remain in the whole system all the time.^42–44 Meanwhile, researchers have found that the rate of the auto-oxidation process is different from that under the action of metal for lubricating oil.⁴⁵ For example, zinc, nickel, and aluminum could act as auto-oxidation inhibiting agents when the peroxide concentration is low,^46,47 while iron could accelerate the rate of oil auto-oxidation owing to its catalytic action.^45,48–50 However, the effects of soluble copper depend on its concentration and other factors.^50,51

Singh et al.⁴⁸ investigated the aging characteristics of base oil under the situation of containing or not containing diarylamine antioxidants. Their results agree with those of earlier researchers because the acceleration of oil aging in tribology experiments is attributed to the catalytic action of iron. Simultaneously, they found that Ar₂NH acted as an effective antioxidant under both tribological oxidation conditions and auto-oxidation processes. It is confusing to us that if the antioxidation performance of Ar₂NH is unchanged in the two different environments, the retarding results should be evidently different for the participation of iron in steel-on-steel lubricated sliding. Moreover, we found that the addition of Ar₂NH to oil provides an antifriction protective graft and reduces the wear of iron. However, the study was not conclusive on which factor—the radical scavenging action, the masking action of Ar₂NH to inhibit the catalytic action of iron, or a combination of the two—is the most important driver of antioxidant action in the friction oxidation process. Spurred by these results, we were curious to see if we could resolve this problem from the perspective of the reaction mechanism. Therefore, we investigated the coordination effects of iron on the antioxidant performance of Ar₂NH by utilizing density functional theory (DFT) calculations.

In this study, we first used the DFT method to search for a more believable and elaborate mechanism for the antioxidation cycle of diarylamine (Ar₂NH). Then, we attempted to answer another question: How would the reaction mechanism be affected if the iron atom or ferric ion coordinates with Ar₂NH? This work is of great significance for understanding the actual antioxidant mechanism of Ar₂NH under most practical lubricating conditions, which is essential for designing or improving new types of diarylamine antioxidants.

Computational details

4,4′-Dimethyldiphenylamine (DMDPA) and the CH₃CH₂CH₂OO˙ radical were chosen as the model compounds for the diarylamine antioxidant and peroxyl radical, respectively. Gaussian 09 program⁵² was used to fully optimize all the structures reported in this study at the B3LYP⁵³ level of theory (298.15 K, 1 atm). The 6-31G(d) basis set was used for geometry optimization. Vibrational frequencies were also subsequently calculated at the same level of theory to ensure each optimized structure as a minimum (N_imag = 0) or transition state (N_imag = 1) and to obtain thermodynamic data. IRC calculations^54,55 were used to confirm the connectivity between transition states and their minima. To obtain more reliable relative energies, single-point energy calculations for all optimized structures were performed by expanding the basis set to 6-311+G(2d,2p). The reported energies are based on these single-point energies, including thermal corrections. The solvation energies were calculated for gas-phase optimized geometries using the SMD solvation model⁵⁶ (hexadecane as a solvent) at the M05-2X/6-31G(d) level of theory,⁵⁷ which was used for parameterizing the SMD model.⁵⁶ However, because the consideration of the solvation did not significantly change the relative energies for the Ar₂NH activation and Ar₂NOR decomposition compared with that from the gas-phase calculation (see Tables S1 and S2 for the energy data in solution), only the gas-phase results at 298.15 K are reported here. The radicals were calculated with an unrestricted wave function. The spin state of the calculated species was optimized to the lowest spin state in energy.

Results and discussion

Activation of Ar₂NH

Although many mechanisms have been proposed to explain the antioxidant process of diarylamines, the viewpoint that the first reaction step is the activation of Ar₂NH by ROO˙ is not controversial. Therefore, the activation mechanism of Ar₂NH was first calculated. In the process, Ar₂NH is converted into Ar₂N˙ radical via homolysis of the N–H bond upon an attack of the ROO˙ radical (Scheme 2, path 1a). Therefore, the bond dissociation energy (BDE) in Ar₂N–H (or ArO–H) has been widely considered an important factor in determining the efficacy of an antioxidant, since the weaker the N–H (O–H) bond, the faster the reaction with free radicals.²⁶ In addition, large amounts of oxygen molecules are present in the system, which may participate in the activation reactions. This situation is also considered (path 1b in Scheme 2). The corresponding reaction energies for paths 1a and 1b are shown in Table S1. Certainly, various radicals exist in the system besides ROO˙, such as alkyls (R˙) and alkoxyls (RO˙). The activation of Ar₂NH by these radicals is inevitable in lubricant degradation. However, activation by ROO˙ is still expected to dominate because the steady-state concentration of ROO˙ is much higher than that of R˙ and RO˙ under most conditions of oxidative degradation.^4,41,58 Therefore, we discuss here the ROO˙-mediated activation of Ar₂NH.

The computed energy profile for the two pathways (paths 1a and 1b) about the activation of Ar₂NH is shown in Fig. 1. In path 1a, pre-reaction complex 1^1a is formed at first with a relative energy of 6.6 kcal mol⁻¹. Then, ROO˙ radical abstracts the hydrogen atom of the N–H bond in Ar₂NH directly via the transition state TS12^1a with an activation energy barrier of 14.2 kcal mol⁻¹ to form the post-reaction intermediate 2^1a, which subsequently converts into P^1a (a combination of Ar₂N˙ and ROOH). Although the reaction energy in path 1a is equal to 0.0 kcal mol⁻¹, the reaction could be considered easy on the dynamics for the low energy barrier. In path 1b, the reaction begins with the formation of 1^1b, which is a complex of Ar₂NH with O₂. Then, 1^1b goes through TS12^1b featuring a concerted event: the cleavage of the N–H bond and formation of O1–H as well as O2–C1 bonds (see Chemdraw-type structure in Fig. 1 for the atom numbering). This step has a Gibbs free energy barrier of 9.6 kcal mol⁻¹ and generates 2^1b, in which the shape and aromaticity of the activated phenyl ring change. The newly formed 2^1b subsequently undergoes an isomerization transition state, TS23^1b_Iso, with a Gibbs free energy barrier of 4.2 kcal mol⁻¹ to break its weak N⋯H interaction and give 3^1b_Iso. Although the relative energy of 3^1b_Iso is slightly higher than that of 2^1b, such an isomerization is beneficial for the H atom of the dangling O1–H bond to interact with the ROO˙ radical. The reaction of ROO˙ with 3^1b_Iso occurs via TS45^1b_H with an activation energy barrier of 18.6 kcal mol⁻¹ to generate 5^1b_H. The hydrogen transfer process is the rate-determining step of the entire pathway. 5^1b_H converts into 6^1b_H by releasing ROOH. Then, 6^1b_H undergoes cleavage of the C1–O2 bond to regenerate oxygen (P^1b in Fig. 1). This step occurs via TS78^1b with a free energy barrier of 1.9 kcal mol⁻¹. This result suggests that oxygen participates in the reaction as a catalyst. We chose singlet oxygen as the reactant owing to its higher activity and triplet oxygen (in P^1b) as the product owing to its better stability. By comparing the whole pathways of 1a and 1b, path 1a is more kinetically favorable (14.2 vs. 18.6 kcal mol⁻¹), and path 1b has a significant exergonic character. Consequently, we suggest that oxygen may participate as a catalyst in the activation reaction of Ar₂NH by ROO˙, which is a feasible process.

Generation of Ar₂NOR

Alkoxyamine is an important intermediate in the process of inhibiting oxidation by Ar₂NH. The possible pathways for the formation of Ar₂NOR are simulated, as shown in Scheme 3. We only investigate these reactions from the viewpoint of thermodynamics since they are rapid radical reactions. Ar₂N˙ could react with O₂¹ to yield Ar₂NO˙ accompanied by significant heat release (reaction 2a). In addition, Ar₂N˙ may capture ROO˙ to produce Ar₂NOOR, which is considered feasible to break the Ar₂NO–OR bond to form Ar₂NO˙ as well (reactions 2b and 2c). The reaction of Ar₂N˙ with ROO˙ is endergonic slightly (2.5 kcal mol⁻¹) from the view of change in Gibbs free energies, while it is exothermic from the point of enthalpies. Comparing the two pathways for the formation of Ar₂NO˙, reaction 2a holds an absolute advantage. The generated Ar₂NO˙ could convert into Ar₂NOR by scavenging R˙ easily (reaction 2d). These results indicate that the generated Ar₂NO˙ radicals are likely to be taken away, which is consistent with the experimental results, that is, the sustained low concentration of Ar₂NO˙.²⁷ Simultaneously, Ar₂N˙ could directly react with RO˙ to yield Ar₂NOR (reaction 2e). The reaction is also exergonic. Therefore, the pathways shown in Scheme 3 are likely to take place to produce Ar₂NOR with respect to the features of radical reactions and thermodynamics. The pathway is more inclined to follow reaction 2a. The results do not agree with Jensen et al.²⁷ who suggest that the activation product Ar₂N˙ could mainly react with another ROO˙ to yield Ar₂NO˙, which could further react with R˙ to produce Ar₂NOR eventually. The results also illustrate that the formation of Ar₂NOR is thermodynamically favored.

Decomposition of Ar₂NOR

Regeneration of Ar₂NH

The crux of the catalytic antioxidation mechanism is to clarify how Ar₂NH is regenerated and then re-enter the catalytic cycle. The experimental results²⁷ indicate that the regeneration of the parent amine comes from alkoxy amine intermediates. Thus, we suppose that the regeneration of Ar₂NH occurs via the reactions of Ar₂N˙, which is the primary product of Ar₂NOR decomposition. Consequently, we calculated four pathways in which Ar₂N˙ reacts with four substrates (ROO˙, ROOH, R˙, and R), which exist in the reaction system to yield Ar₂NH, as shown in Scheme 6. The reaction mechanism for all four pathways is the hydrogen transfer process. The computed energy profile is shown in Fig. 4.

As shown in Fig. 4, path 5a describes the reaction of Ar₂NH with ROO˙ to produce Ar₂NH, propylene, and oxygen. The reaction (green line) is impossible because of its excessive activation energy barrier, 38.6 kcal mol⁻¹, although the reaction is exothermic. Path 5d demonstrates that the reaction of Ar₂NH with R is also impossible owing to its higher activation energy barrier (39.3 kcal mol⁻¹), which is shown in the red line. Along with path 5b (blue line), the regeneration of Ar₂NH starts with the coordination of Ar₂N˙ with ROOH to form 1^5b, which comes with the absorption of heat (4.4 kcal mol⁻¹). 1^5b goes through a hydrogen-transfer transition state with a Gibbs free energy barrier of 15.8 kcal mol⁻¹, TS12^5b, leading to 1^5b, which separates into Ar₂NH and ROO˙ (P^5b). The reaction is kinetically feasible. However, in view of the thermodynamic feature, path 5b (reaction of ROOH) is reversible. Therefore, path 5b is unfavorable owing to the regeneration of Ar₂NH. In path 5c (black line), the coordination of Ar₂N˙ with R˙ yields 1^5c and is endergonic by 7.6 kcal mol⁻¹. Then, intermediate 1^5c also undergoes a hydrogen-transfer transition state, TS12^5c, to produce 2^5c with a free energy barrier of 12.8 kcal mol⁻¹. Intermediate 2^5c tends to convert into Ar₂NH with the release of propene (P^5c). The results suggest that path 5c is kinetically favorable compared with path 5b. Moreover, path 5c is significantly exergonic (energy release of −45.1 kcal mol⁻¹). Therefore, the regeneration of Ar₂NH is derived from the reaction of Ar₂N˙ with R˙ (path 5c), which re-enters the reaction system to trap peroxyl radicals.

Catalytic inhibition mechanism

In summary, we proposed a detailed mechanism for catalytic inhibition by Ar₂NH and its derivatives. As shown in Scheme 7, diarylamine, Ar₂NH, first captures a peroxyl radical (ROO˙) by donating its N–H hydrogen atom to an ROO˙ to produce hydroperoxide (ROOH) and converts itself into diarylaminyl radical, Ar₂N˙. It is noteworthy that oxygen may participate in the reaction, which acts as a catalyst. Afterwards, Ar₂N˙ can react with O₂ or another ROO˙ to yield Ar₂NO˙, which can turn into alkoxydiarylamine (Ar₂NOR) readily, of which the reaction with O₂ is dominating. Meanwhile, Ar₂N˙ can directly react with RO˙ to form Ar₂NOR, but the concentration of RO˙ is low. Therefore, the formation of Ar₂NOR is mainly through the reaction of Ar₂NO˙ with R˙. Next, Ar₂NOR can decompose via β-site hydrogen atom to another ROO˙, followed by N–O bond cleavage, leading to the formation of Ar₂N˙ and propionaldehyde (β-H mechanism). Ar₂N˙ then can react with the R˙ radical to produce propylene and Ar₂NH, which will re-center in the cycle and complete the catalytic inhibition process. In addition, the decomposition of part Ar₂NOR will likely follow the γ-H mechanism, i.e., transfer their γ-site hydrogen atom to the ROO˙ radical to form Ar₂NO˙ and propylene. Ar₂NO˙ could also re-enter the catalytic cycle to transform itself into Ar₂NOR. This is why the experimentally observed concentration of Ar₂NO˙ is maintained at a low level. One complete inhibition cycle at least traps three ROO˙ radicals and two R˙ radicals. In general, one of the features of the inhibition cycle is the decomposition mechanism of Ar₂NOR, which we believe occurs through reactions with another ROO˙ rather than thermal decomposition. What's more, we suggested that Ar₂N˙ radicals are also quite important intermediates. The catalytic inhibition cycle involves the regeneration of three species: Ar₂NO˙, Ar₂N˙ and Ar₂NH.

By analyzing the calculated results, we found that the β-H transfer reaction in the decomposition of Ar₂NOR through the β-H mechanism is the rate-determining step for the whole catalytic inhibition pathway. Thus, the –CH₃ substituent groups in the 4 and 4′-sites are changed to assess the influence of such substituents on these reactions. The substituted groups and calculated results are shown in Table 1.

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Comparing the results in Table 1, the activation energy barriers for the reactions of Ar₂NOR, which are substituted by electron-donating groups (–CH₃, –tBu, and –OCH₃) with ROO˙, are almost the same, about 26.5 kcal mol⁻¹. However, the activation energy barrier of the β-H transfer reaction increases when the 4 and 4′-sites are substituted by –NO₂ although the change is not obvious, that is 28.2 kcal mol⁻¹. These results could provide some enlightenment that the substituted electron-withdrawing groups are averse to the reactions when compared with the electron-donating groups. Valgimigli and Pratt observed that incorporating electron-withdrawing groups can enhance the oxidation potential of diarylamine antioxidants.⁵⁹ This modification, however, results in only a modest reduction in reactivity, which is consistent with our findings. Furthermore, researchers found that the substitution of electron-donating groups decreases the N–H bond dissociation energy of aniline, whereas electron-withdrawing groups have the contrary effect.^60,61 However, introducing nitrogen atoms into the aromatic rings of the phenolic compounds can render them more stable to single-electron oxidation, thereby enabling the substitution of strong electron-donating groups.⁵⁹ Generally speaking, we suggested that the substituted electron-donating groups are advantageous for the antioxidant performance of Ar₂NH in the catalytic inhibition cycle. The results may suggest the development of new diarylamine antioxidants.

Coordination of Fe(III) and Fe atom

The aforementioned studies confirmed the catalytic antioxidant mechanism of Ar₂NH, including three main reaction steps: (i) activation of Ar₂NH by reacting with ROO˙, (ii) decomposition of Ar₂NOR following the β-H mechanism, and (iii) regeneration of Ar₂NH through reaction of Ar₂N˙ with R˙. Here, the coordination effects of Fe(III) or Fe atom for the mechanism of catalytic inhibition by Ar₂NH are investigated.

First, the possible complex structures of Ar₂NH coordinating with Fe(III) or Fe atom are optimized. The most stable isomers (i.e., the lowest relative energy structures) are chosen as the models (Fig. 5). The other optimized isomers with higher energies are provided in Fig. S1. Meanwhile, the corresponding binding energy (energy difference between the metal complex and the energy sum of metal and Ar₂NH) is reported in Fig. 5.

As shown in Fig. 5, Fe(III) coordinates to one benzene ring of Ar₂NH to form a η⁶-complex, Ar₂NH_Fe(III), which is a quartet. Compared to Ar₂NH, the N–H bond in this complex is slightly elongated from 1.01 Å to 1.02 Å, while the C1–N–C2 angle increases from 129.7° to 132.3°. Additionally, the C1–N and C2–N bonds become asymmetric owing to the interaction with Fe(III), which are equal in Ar₂NH (1.40 Å). In the case of the Fe atom, a multiple–coordinate complex was located where the Fe atom interacts with one benzene ring and a C atom of another benzene moiety in Ar₂NH. In Ar₂NH_Fe, the vertical distance between the Fe atom and the centroid of the coordinating benzene ring is 1.48 Å. Compared with Ar₂NH, the C1–N bond length increases from 1.40 Å to 1.44 Å, while the C1–N–C2 angle decreases from 129.7° to 114.2°. It is noteworthy that the binding between Fe(III) or Fe atom and Ar₂NH could be strong, as suggested by the binding energies shown in Fig. 5. This result indicates that diarylamines are facile to chelate with Fe(III) or Fe atom and prefer the relatively electron-deficient Fe(III). This makes us further investigate the reactions of Fe(III) or Fe atom coordinating with Ar₂NH.

Coordination effects of Fe(III) and Fe atom for activation of Ar₂NH

First, the coordination effects of Fe(III) and Fe atoms on the activation process of Ar₂NH by reacting with ROO˙ have been studied. As shown in Fig. 6, the activation mechanism is considered a hydrogen atom transfer process in which diarylamines donate their N–H hydrogen atom to an ROO˙ radical. Compared with bare Ar₂NH, the metal complex-mediated reaction becomes more kinetically feasible, as suggested by their lower activation free energy barrier (14.2 vs. 6.5 and 2.5 kcal mol⁻¹). In the case of the Fe(III) complex, the pathway starts with the formation of a quite stable pre-reaction complex 1^1a_Fe(III), accompanied by heat release. Then, 1^1a_Fe(III) goes through a hydrogen atom transfer transition state, TS12^1a_Fe(III), to yield intermediate 2^1a_Fe(III) with a low energy barrier (2.5 kcal mol⁻¹). Although 2^1a_Fe(III) is slightly less stable than 1^1a_Fe(III), even higher in energy than TS12^1a_Fe(III), the accumulation of 1^1a_Fe(III) is beneficial to the generation of 2^1a_Fe(III). In addition, the separation reaction of post-reaction complex 2^1a_Fe(III) needs to absorb heat, which converts 2^1a_Fe(III) into P^1a_Fe(III) (Ar₂N˙_Fe(III) and ROOH), which means that the products are inclined to exist as complex 2^1a_Fe(III). However, there are several other radical species in the system, such as the RO˙ radical. Therefore, 2^1a_Fe(III) could release a ROOH accompanied by RO˙ attack to form Ar₂NOR_Fe(III), which is thermodynamically favorable. A similar process is also obtained for the case of Ar₂NH_Fe, which exhibits a higher free energy barrier than that for Ar₂NH_Fe(III) (6.5 vs. 2.5 kcal mol⁻¹), finally leading to P^1a_Fe (Ar₂N˙_Fe + ROOH) or Ar₂NOR_Fe after an attack by the RO˙ radical. Obviously, compared with bare Ar₂NH, the coordination of Fe(III) or Fe atom makes the activation of Ar₂NH easier.

Coordination effects of Fe(III) and Fe atoms on the decomposition of Ar₂NOR

The aforementioned results about the decomposition of Ar₂NOR demonstrated that the β-H mechanism is favorable in both kinetics and thermodynamics, by which Ar₂NOR converts into Ar₂N˙. The possibility of the γ-H mechanism cannot be neglected although it is not dominant compared with the β-H mechanism. Therefore, decomposition pathways of Fe(III) (7a) or Fe atom (7b) coordinating Ar₂NOR complexes are calculated according to both β-H and γ-H mechanisms (Fig. 7)

As depicted in Fig. 7a, attempts to locate both pre-reaction complexes 1^4a_Fe(III) and 1^4b_Fe(III) along with β-H and γ-H mechanisms were fruitless. Thus, the two pathways directly start with the transfer of β-site or γ-site hydrogen atoms in Ar₂NOR_Fe(III) to ROO˙ and deliver the stable intermediates 2^4a_Fe(III) (−32.4 kcal mol⁻¹) or 2^4b_Fe(III) (−39.6 kcal mol⁻¹). It is noteworthy that the two processes go through barrierless transition states TS12^4a_Fe(III) and TS12^4b_Fe(III), respectively. Then, 2^4a_Fe(III) involved in the β-H mechanism undergoes its N–O bond cleavage to yield 3^4a_Fe(III) with coordinating propionaldehyde. 3^4a_Fe(III) is so stable that the dissociation of propionaldehyde is considerably endergonic (109.5 − 36.9 = 72.6 kcal mol⁻¹). However, 2^4b_Fe(III) involved in the γ-H mechanism needs to absorb an energy of 21.8 kcal mol⁻¹ to afford 3^4b_Fe(III) by releasing ROOH. Then, 3^4b_Fe(III) goes through TS34^4b_Fe(III) with an energy barrier of 13.1 kcal mol⁻¹ to finally give P^4b_Fe(III) via C–O bond cleavage. It is noteworthy that during the conversion of 3^4b_Fe(III) to P^4b_Fe(III), the energy barrier was calculated to be 20.6 kcal mol⁻¹ when considering ROOH coordination. With respect to such an energy barrier for the γ-H mechanism, the decomposition of Ar₂NOR_Fe(III) kinetically tends to follow the β-H mechanism.

As shown in Fig. 7b, the decomposition of Ar₂NOR_Fe starts with the interaction of ROO˙ with β- or γ-H atom in Ar₂NOR_Fe to yield intermediates 1^4a_Fe and 1^4b_Fe, whose relative energies are almost the same (8.2 and 8.4 kcal mol⁻¹, respectively). Then, 1^4a_Fe (or 1^4b_Fe) goes through a β-site (or γ-site) hydrogen atom transfer transition state, TS12^4a_Fe (or TS12^4b_Fe), leading to intermediate 2^4a_Fe (or 2^4b_Fe), with a Gibbs free energy barrier of 10.7 kcal mol⁻¹ (or 14.8 kcal mol⁻¹). Then, 2^4a_Fe is transformed into 3^4a_Fe by releasing ROOH. This step is endergonic by 8.4 kcal mol⁻¹. Intermediate 3^4a_Fe could undergo N–O bond cleavage via TS34^4a_Fe with a low free energy barrier of 0.9 kcal mol⁻¹ to afford more stable intermediate 4^4a_Fe, which is further feasibly converted to P^4a_Fe (Ar₂N˙_Fe + propionaldehyde). Similarly, 2^4b_Fe tends to convert into 3^4b_Fe by releasing ROOH. Then, 3^4b_Fe undergoes C–O bond cleavage via TS34^4b_Fe to afford 4^4b_Fe, which further generates P^4a_Fe (Ar₂NO˙_Fe + propene) by overcoming a free energy barrier of 6.4 kcal mol⁻¹. Compared with the β-H and γ-H mechanisms shown in Fig. 7b, the decomposition of Ar₂NOR_Fe could preferably follow the β-H mechanism because of its lower free energy barrier and more significant exergonic features. Therefore, the coordination of Fe(III) or Fe atom does not change the decomposition pathway of Ar₂NOR, which always follows the β-H mechanism. The calculated energy profiles for the decomposition of Ar₂NOR with coordinating Fe(III) or Fe atom are shown in Fig. S2.

Coordination effects of Fe(III) and Fe atom for the regeneration of Ar₂NH

The above-mentioned results indicate that the regeneration of Ar₂NH occurs via the reaction of Ar₂N˙ with R˙ (Scheme 6 and Fig. 4). The coordination effects of Fe(III) and Fe atoms on this reaction are investigated here. The calculated energy profile is shown in Fig. 8. Simultaneously, we also calculated other possible regeneration pathways of Ar₂NH with coordinating Fe(III) or Fe atom to confirm the most favorable pathway. The results indicate that the coordination of Fe(III) or Fe atom does not change the favorable reaction pathway for the regeneration of Ar₂NH (Fig. S3).

As shown in Fig. 8, the regeneration of Ar₂NH goes through a C–H hydrogen atom transfer from R˙ to Ar₂N˙ accompanied by the release of propylene with an energy barrier of 12.8 kcal mol⁻¹. After coordinating with the Fe atom, the activation energy barrier is reduced to 9.9 kcal mol⁻¹. The reaction of Ar₂N˙_Fe with R˙ is also exergonic although the subsequent discoordination of propylene requires an energy of 7.2 kcal mol⁻¹. The regenerated Ar₂NH_Fe could capture ROO˙ to take part in the antioxidation cycle.

It is noted that in the case of Fe(III), attempts to locate reaction intermediates were fruitless along with the regeneration pathway. As shown in Fig. 8, the reaction of Ar₂N˙_Fe(III) with R˙ directly goes through a barrierless H-transfer transition state TS12^5c_Fe(III) to yield Ar₂NH_Fe(III), accompanied by the release of propylene (red line in Fig. 8). It is noteworthy that the resulting ˙CH₂CH₂CH₃ could turn into its isomer, ˙CH(CH₃)₂, to participate in the reaction. Therefore, the coordination of Fe(III) or Fe atom could accelerate the regeneration of Ar₂NH, especially for the Fe(III) case. To sum up, the results indicate that the coordination of Fe(III) or Fe atom could promote the antioxidant process of Ar₂NH, including the activation of Ar₂NH, decomposition of Ar₂NOR, and the regeneration of Ar₂NH, especially in the case of Fe(III).

Conclusion

Diarylamines (Ar₂NH) are highly effective antioxidants under high temperatures, making them highly employed in lubricating oil over a wide range of operating conditions. The origin of their high efficiency has attracted considerable attention. This study proposed a detailed catalytic inhibition mechanism of Ar₂NH through DFT calculations. The results show that the reaction of the ROO˙ radical with Ar₂NH leads to the activation of Ar₂NH. It is noteworthy that oxygen may serve as a catalyst to participate in this reaction. The key intermediate Ar₂NOR could be decomposed via the β-H mechanism by reacting with the ROO˙ radical, resulting in the formation of Ar₂N˙ radical. This mechanism differs from the previously proposed thermal decomposition process. The resulting Ar₂N˙ could subsequently react with an R˙ radical to regenerate Ar₂NH, which reenters the reaction system to complete the catalytic cycle. In addition, the substitution of electron-withdrawing groups on the phenyl ring in Ar₂NH may reduce the antioxidant ability of Ar₂NH.

The presence of metal in oil is ubiquitous in most practical lubricating systems. These metals could improve the antioxidant performance of Ar₂NH. It is reasonably considered that Ar₂NH antioxidants are inclined to exist as complexes with a coordinating metal ion or atom. It is found that the coordination of Fe(III) ion or Fe atom could make the catalytic inhibition process of Ar₂NH more kinetically feasible, especially for the case of Fe(III) ion, by increasing its radical scavenging ability in practical situations. This study provides a better understanding of the high efficiency of diarylamine in catalytic oil oxidation inhibition.

Author contributions

Junming Wang: conceptualization and writing – original draft. Weiguo Xue: investigation and formal analysis. Zhuozheng Wang: calculation, writing – review and editing. Hao Li: software and formal analysis. Huiying Lv: data curation and validation. Chaoliang Wei: investigation, writing – review and editing. Qingwei Kong: resources, writing – review and editing. Xiaowei Xu: methodology, writing – review and editing. Kebin Chi: investigation, writing – review and editing. Dejun Shi: data curation, writing – review and editing. Yufeng Liu: software, writing – review and editing. Tuanle Li: validation, writing – review and editing. Yi Luo: supervision, project administration, writing – review and editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data underlying this study are available in the published article and its SI.

The data supporting this article have been included. See DOI: https://doi.org/10.1039/d5nj02543e

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Footnote

† Qingwei Kong's current address: The No. 2 Middle School of Sanhe, Sanhe 065200, China.

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