In-situ catalysis of green lubricants into graphitic carbon by iron single atoms to reduce friction and wear

Abstract

Reducing friction and wear in moving mechanical systems is essential for their intended functionality. This is currently accomplished by using a large variety of anti-friction and anti-wear additives, that usually contain sulfur and phosphorous both of which cause harmful emission. Here, we introduce a series of diesters, typically dioctyl malate (DOM), as green and effective anti-friction and anti-wear additives which reduce wear by factors of 5-7 and friction by over 50% compared to base oil when tested under high pressures. Surface studies show that these impressive properties are primarily due to the formation of a 30 nm graphitic tribofilm that protects rubbing surfaces against wear and hence provides low shear stress at nanoscale. This graphitic tribofilm is prone to form from diesters derived from short-chain carboxylic acid due to their lone pair effect, which stabilizes the carbon free radicals. Furthermore, the formation of this tribofilm is catalyzed by nascent iron single atoms, which are in-situ generated due to the mechanochemical effects during sliding contact. Computational simulations provided additional insights into the steps involved in the catalytic decomposition of DOM by iron and the formation of a graphitic carbon tribofilm. Due to its anti-friction and wear properties, DOM holds promise to replace conventional additives, and thus provides a green and more effective alternative for next-generation lubricant formulations.

Introduction

Friction and wear result in significant energy and material losses in moving mechanical systems^1,2. This is commonly alleviated using liquid lubricants³ blended with anti-friction and anti-wear additives⁴. Usually, lubricant additives play a crucial role in governing tribological performance, especially during boundary lubrication where the asperities can collide directly and very frequently⁴. In recent decades, zinc dialkyl dithiophosphate (ZDDP), a typical lubricant additive, has been widely used in engine oils as an anti-wear agent. Its performance can be attributed to the in-situ formation of a patchy tribofilm on rubbing surfaces, preventing a direct metal-to-metal contact during the rubbing process^5,6,7 and hence reducing wear. However, the sulfur and phosphorus in ZDDP are poisonous to the pollutant-reducing catalytic converters in all motored vehicles^8,9. In addition, ZDDP usually cannot provide a satisfactory friction-reducing performance; hence, it must be combined with additional friction modifiers, such as molybdenum dithiocarbamates. In addition to ZDDP, other nanomaterials have been extensively studied as lubricant additives in past decades. For example, typical nano-carbon nanomaterials, such as graphene^10,11, carbon nanotubes¹², and carbon quantum dots^13,14 exhibit excellent friction-reducing and anti-wear performance. However, their application is limited because they cannot be well-dispersed in lubricants, as they agglomerate or separate from the base oil over time^15,16. As a result, they cannot enter the contact area and adhere to surfaces because of their larger size and chemical inertness⁴. Therefore, developing environment-friendly additives that are readily soluble in lubricants and provide excellent tribological performance will be essential for achieving long-range efficiency and reliability goals of motored vehicles.

Generally, a desirable lubricant additive is expected to adsorb strongly on the tribopair surfaces via physisorption or electrostatic interactions, hydrogen bonding or coordination bonding^17,18, and hence it can effectively protect the solid–solid contacts at the initial stage of sliding. Additionally, an ideal lubricant additive should be chemically reactive such that it can be further converted into a low-friction and highly protective tribofilm via the tribochemical reaction during the rubbing process^19,20. Due to strong chemical bonding, such a tribofilm can provide long-lasting reductions for friction and wear and this process can continue as the lost film is very quickly repaired or replenished through the robust tribochemical reaction.

Amphiphilic molecules, which have been extensively studied by tribologists, are composed of polar head groups and nonpolar tail groups and are widely used as organic friction modifiers in commercial lubricants^21,22. Typical amphiphilic molecules, including fatty alcohols, fatty acids and glycerol monooleate (GMO), usually have no sulfur and phosphorus components, and have been used as green lubricant additives to circumvent harmful effects of ZDDP. Meanwhile, these additives can effectively reduce friction and wear by up to 45% and 83%, owing to the formation of a tribofilm, such as a carboxylate on the steel surface²². Furthermore, certain amphiphilic additives can achieve a superlubricity state with friction coefficient lower than 0.01, through the formation of a tribofilm^23,24. Among these amphiphilic molecules, fatty alcohols were found to exhibit higher friction and wear than fatty acids owing to their lower adsorption strength on metal surfaces²⁵. Accordingly, we hypothesize that if the fatty alcohol is chemically modified into a molecule that can readily adsorb and strongly bond to the rubbing surface, the tribological performance of the modified fatty alcohols will be substantially improved. Here we select a fatty alcohol molecule (i.e., octanol, see Fig. 1a) and chemically grafted it with malic acid to form the dioctyl malate (DOM in Fig. 1a). As malic acid contains multiple chemically active carboxylic acid and alcohol groups, it is anticipated to enhance the adsorption of DOM on a sliding surface thus leading to a good anti-friction and wear performance^26,27. DOM is used as an additive in an ultra-low viscosity oil (i.e., polyalphaolefin (PAO2), referred as PAO hereafter) and tested in the boundary lubrication regime where frequent metal-to-metal contact and hence high-friction and -wear are anticipated.

Fig. 1: Tribological performance of polyalphaolefin (PAO) with various additives.

a Molecular structure of the additives. b Schematic of a ball-on-disc tribometer with the reciprocating mode. c Friction coefficient of neat PAO and PAO containing various additives, including 5 wt% octanol, 5 wt% dioctyl malate (DOM), and 5 wt% oleic acid (OA). The test was conducted under 36 N at 30 °C, and the stroke length was 1 mm with a frequency of 10 Hz. The break in Y axis is from 0.005 to 0.09. d Height profiles (position marked in Supplementary Fig. 5), and e optical images of wear tracks on discs lubricated by neat PAO, 5 wt% octanol in PAO, 5 wt% OA, and 5 wt% DOM in PAO. f Wear volume of the balls lubricated by different lubricants. The error bars represent the standard deviation based on triplicate measurements. g The friction coefficient of neat PAO and 5 wt% DOM in PAO under a load increasing stepwise from 36 to 176 N. The load increased by 20 N per 5 min, as shown in the blue curve. h Friction coefficient of 5 wt% DOM and its surface coverage of islands versus time. The calculation of surface coverage can be found in Supplementary Fig. 13c. Source data are provided as a Source Data file.

Results and discussion

The macrotribological performance

Tribological tests on PAO and DOM additized PAO (Fig. 1a) were carried out using a steel ball on steel disc tribometer (Optimol Instruments, SRV4) in a reciprocating mode (Fig. 1b). The concentration-dependent friction tests revealed that the addition of 5% DOM into PAO exhibited the best performance (Supplementary Fig. 1), which substantially reduced friction coefficient (Fig. 1c, from ~0.25 to ~0.11), wear track depth (Fig. 1d, from ~1.5 µm to ~0.2 µm), width (Fig. 1e, from ~420 µm to ~224 µm), and wear volume (Fig. 1f, from ~27 × 10⁻⁵ mm³ to ~3.7 × 10⁻⁵ mm³). Note that the low friction and wear of 5 wt% DOM containing PAO persist even under a heavy load of 176 N (Fig. 1g, Supplementary Fig. 2), corresponding to a maximum Hertz contact pressure of 2.78 GPa. In comparison, neat PAO exhibited a steeply increasing friction coefficient (i.e., 0.82) accompanied by severe wear losses (Supplementary Fig. 2a) once the load reached 76 N in about 10 min, indicating lubrication failure. PAO with other amphiphilic additives (i.e., octanol, and oleic acid (OA)) also showed some reduction in friction and wear under a 36 N test (Fig. 1c, f, Supplementary Figs. 3–7), but they were still much higher than those observed on DOM with PAO oil. The lubrication mechanisms of amphiphilic molecules, like oleic acid, have been extensively studied and are commonly attributed to the formation of an adsorbed layer on the solid surface via their polar head group, which helps to reduce friction and wear^28,29. From Fig. 1e and (Supplementary Fig. 7, it is clear that deep scratches and wear debris are present within and around wear tracks (especially toward the end of strokes) of PAO, 5 wt% octanol, and 5 wt% OA; however, these were noticeably absent with 5 wt% DOM in PAO oil, further suggesting a much better anti-wear property provided by DOM additive.

Additionally, a comparison with conventional industrial additives, including GMO and ZDDP, further highlights DOM’s better performance. The friction coefficients of 5 wt% GMO and 5 wt% ZDDP were 0.20 and 0.14, respectively (Supplementary Fig. 3), both significantly higher than that achieved with 5 wt% DOM. While the wear track width and wear volume of 5 wt% ZDDP were comparable to those of 5 wt% DOM (Supplementary Fig. 4c, d), DOM is free of sulfur and phosphorus, making it a much more environmentally friendly option. Notably, even at a low concentration of 1 wt%, DOM also exhibits a much lower friction coefficient and no visible wear scratches compared to ZDDP and GMO (Supplementary Fig. 6), further demonstrating the better performance of DOM. Therefore, the performance of this green DOM additive, combined with its sustainable composition, highlights its great potential as a replacement for conventional lubricant additives like ZDDP and GMO.

After the tribological test, the wear track was rinsed with hexane to eliminate lubricant residue on the surface. Note that the rinsing will not affect the surface chemistry/mechanical properties of the wear track (Supplementary Fig. 8). Interestingly, while neat PAO (Supplementary Fig. 9), 5 wt% OA (Supplementary Fig. 10), and 5 wt% octanol (Supplementary Fig. 11) exhibited similar wear track appearances before and after rinsing, whereas 5 wt% DOM in PAO showed a gray, patchy structure in the wear track after rinsing (Supplementary Fig. 12). Notably, this gray patchy area is higher than its surrounding area in the wear track (Supplementary Fig. 12c), suggesting a raised island-like structure formation. Interestingly, the surface coverage of these islands in the wear track gradually increased from 30 s to 5 min (Supplementary Fig. 13), which coincided with the decreasing tendency of friction coefficient (Fig. 1h). This suggests that the formation of these island-like structures may contribute to the anti-friction- and -wear performance of DOM.

The nanomechanical properties on the wear tracks

Tribological tests suggest patchy island-like film formation on the rubbing surface by 5 wt% DOM, which has minimized direct steel–steel contacts during rubbing. The mechanical properties of these islands were examined using nanoindentation tests on the three highlighted areas (with circles) shown in Fig. 2a. The penetration depth was fixed at 40 nm. The maximum nanoindentation load applied to the island area reaches 220 µN (Fig. 2b) which is significantly lower than those measured in the unrubbed or no-island-like areas inside the wear track. This suggests that the island film has a considerably lower Young’s modulus and hardness than the other two areas (Supplementary Fig. 14). Note that the measured Young’s modulus and hardness of the island-like film in Supplementary Fig. 14 may be overestimated due to the 40 nm indentation depth possibly exceeding the film’s actual thickness, but there is no doubt that the island-like film qualitatively exhibits lower Young’s modulus and hardness relative to the other two areas. Interestingly, the no-island-like regions inside the wear track displayed higher hardness and Young’s modulus than unrubbed area. This enhancement can be attributed to the localized contact pressure, shear stress and thermal effects during sliding, which strengthened the mechanical properties in these regions^30,31,32. Additionally, the load–time curve on the island-like areas exhibits a decreasing load trend from 10 to 15 s (Fig. 2c), while the tip maintained a depth of 40 nm. This behavior indicates stress relaxation behavior within the island-like film, indicative of its viscoelastic property. Usually, such stress relaxation is observed in metallic materials at high temperatures or in polymeric materials at room temperature³³. Therefore, the island-like area is potentially composed of a polymer-like layer exhibiting viscoelastic properties. Notably, this viscoelastic behavior was not observed in the unrubbed or no-island area (Fig. 2c, Supplementary Fig. 15).

Fig. 2: Nano-mechanical and surface chemical analysis on the wear track formed by 5 wt% dioctyl malate (DOM).

a Optical microscopy image of wear track. The three marked areas are denoted as on-island area inside wear, no-island area inside wear, and unrubbed area, where indentation and atomic force microscopy (AFM) tests were performed. b Load-depth, and c load-time curves during the indentation tests on three areas in (a). d AFM frictional signal tendency from 1st scanning to 110th scanning on a 10 µm × 10 µm island area. The delta $f$ was calculated by the difference between the friction at the n-th scan (${f}_{n}$) and the friction at the 1st scan (${f}_{1}$), and the error bars represent friction standard deviation extracted from different areas. The insets are the AFM friction images at 1st and 110th scanning. e Histogram of the pull-off force when the AFM tip retracted from the three areas in (a) during the AFM indentation test. f Raman and i Fourier-transform infrared (FTIR) spectra on wear tracks compared to those of other additives. g Optical microscopy images of wear track and h the corresponding Raman G band intensity mapping images. Source data are provided as a Source Data file.

The AFM topography images located at the boundary between the unrubbed and island-like film areas show the typical patchy structure of this film (Supplementary Fig. 16). The friction properties of the film were analyzed using repeated AFM rubbing tests over a 10 µm × 10 µm area under a load of 60 nN. Due to the small radius of the AFM tip (~10 nm), this corresponds to an exceptionally high contact pressure of 2.41 GPa—significantly higher than the contact pressure observed in macro-scale tribological tests (1.64 GPa, as detailed in Supplementary Table 1). This elevated pressure allows for an in-depth investigation of the mechanical properties and wear track surfaces at the nanoscale. Interestingly, while the topography of the island-like film remained the same from the 1st to 110th rubbing cycles (Supplementary Fig. 17a, b), the average friction force decreased substantially during the initial 20 rubbing scans (Fig. 2d), after which it reached a plateau. This suggests that the film is strong against wear by the AFM tip and can provide low friction even at nano-scales. In contrast, the wear track surface of 5% octanol exhibited poor durability under repeated AFM rubbing tests, as evidenced by notable differences in the height profile (Supplementary Fig. 18a, b). Additionally, the repeated rubbed area showed no significant decrease in friction (Supplementary Fig. 18c) and displayed similar frictional properties to its surrounding unrepeated rubbed area (Supplementary Fig. 18i). These observations align with the higher friction and wear observed in macroscale tribological tests for 5% octanol. Further analysis of force–distance curves revealed that the island-like film area exhibited the lowest slope and pull-off force (Fig. 2e, Supplementary Fig. 19), compared to the other two areas^34,35,36. This implies that the island film possesses lower Young’s modulus and adhesion, which contribute to its ability to reduce friction at both nano and macro scale.

The tribochemical reactions on the wear tracks

To unravel the chemical composition of the wear tracks surface, a variety of surface analytical techniques was used on wear tracks. Raman spectra of wear tracks formed in 5 wt% OA and 5 wt% octanol exhibited a distinctive Fe₃O₄ peak at 669 cm⁻¹ (Fig. 2f)^37,38, indicating that these surfaces experienced severe oxidation during sliding. In contrast, with the use of 5 wt% DOM in PAO, Fe₃O₄ peak intensity decreased substantially, and the D and G bands that are typical of graphitic carbon material emerged^39,40,41, especially in the island-like areas. The Raman G band intensity mapping in Fig. 2h showed a distribution that resembles that of the island area in Fig. 2g, further proving the presence of some graphitic carbon material within the island-like films leading to low friction and wear. These films may have also been responsible for protection against oxidation. Further, Fourier-transform infrared (FTIR) spectra show that very little or no traces of C-H and C=O stretching vibrations from the original PAO and DOM are observed in the wear track formed by 5 wt% DOM (Fig. 2i and Supplementary Fig. 20), suggesting the dehydrogenation process and complete conversion of carbon backbone of DOM molecules into the carbon film. Typical sp² C=C stretching originating from the aromatic ring compound⁴² can be found within the wear track formed by 5 wt% DOM containing PAO (Fig. 2i), which further suggests the formation of graphitic carbon.

From Fig. 3a, the surface chemistry of the wear track determined by X-ray photoelectron spectroscopy (XPS) using the layer-by-layer sputtering method shows that 5 wt% DOM exhibits a considerably higher carbon concentration (beyond the top contaminant layer) at depths to 26 nm than those observed in the neat PAO, 5 wt% octanol, and unrubbed area. Note that the carbon in wear track of 5 wt% DOM showed sp² hybridization from 2 to 10 nm depth (Fig. 3d)⁴³, which differs from the C-Fe phase (originate from Fe₃C in steel) from the unrubbed area (Fig. 3e)^44,45, and the sp³ hybridized carbon⁴³ in wear track of neat PAO (Fig. 3f) and 5 wt% octanol (Supplementary Fig. 21). Meanwhile, 5 wt% DOM shows lower oxygen (Fig. 3b) and higher iron (Fig. 3c) concentrations (beyond the top native oxide layer) than those in neat PAO and 5 wt% octanol, and its iron exists in the form of iron (0) from 4 to 36 nm (Fig. 3d), which is similar to the unrubbed area (Fig. 3e)⁴⁶. In contrast, the wear track of neat PAO and 5 wt% octanol exhibits a distinctive iron oxide from depths of 0 to 36 nm (Fig. 3f, Supplementary Fig. 21)^47,48,49. These results indicate that 5 wt% DOM forms a carbon film without an oxidation layer on top of the steel substrate. This film is ~30 nm thick and effectively reduces friction and wear. Conversely, 5 wt% octanol and neat PAO form a thick iron oxide film during rubbing action (Supplementary Fig. 22), which cannot reduce friction or wear effectively. This finding is consistent with the Raman and FTIR spectra.

Fig. 3: The X-ray photoelectron spectroscopy (XPS) analysis on wear track formed by different lubricants.

a Carbon, b oxygen, and c iron atomic concentrations at different depths, obtained by XPS sputter test on wear track of different additives. C 1s and Fe 2p high-resolution XPS spectra on wear track of d 5 wt% dioctyl malate (DOM) in polyalphaolefin (PAO), e unrubbed area, and f neat PAO after normalization. Source data are provided as a Source Data file.

The cross-sectional view of the wear track formed by 5 wt% DOM was observed using transmission electron microscopy (TEM). A typical film (referred as tribofilm hereafter) with a thickness of 30 nm is observed between the Cr top-coating and steel substrate (Fig. 4a), and the thickness matches well with the XPS carbon concentration depth profile in Fig. 3a. Notably, some layered material is observed inside the tribofilm (Fig. 4b), and its lattice fringe spacing distance is approximately 0.39 nm, which is close to the theoretical value of graphene (which is 0.34 nm⁵⁰). EDS elemental mapping images and line scanning show that this tribofilm is rich in carbon (Fig. 4e,f), and its carbon K-edge electron energy loss spectroscopy exhibits typical σ* and π* state (Fig. 4c), corresponding to sp³ and sp² bonding^51,52. Thereby, combined with the Raman and FTIR results, it can be inferred that this tribofilm mainly consists of graphitic carbon. Additionally, the STEM image and corresponding EDS spectrum show that some iron is also atomically distributed inside the tribofilm (red circles in Fig. 4i), suggesting the iron single atoms formation⁵³. The extended X-ray absorption fine structure (EXAFS, Fig. 4k, l, Supplementary Fig. 23, 24) further reveals that the iron single atoms bond with surrounding atoms in the form of -C-O-Fe, which favors their stabilization in the carbon tribofilm. Note that the iron single atoms formation under mechanochemistry effect has been reported in a ball-milling experiment before⁵⁴. The iron single atoms probably arise from the wear debris generated during rubbing and are formed under mechanochemistry⁵⁴. Here, we propose that iron single atoms were largely responsible for the continuous catalysis of DOM molecules leading to graphitic carbon formation, which will be further discussed in the subsequent section.

Fig. 4: Morphology and chemical analysis on the tribofilm formed by 5 wt% dioctyl malate (DOM).

a Cross-sectional transmission electron microscopy (TEM) image of the wear track formed by 5 wt% DOM. b High-resolution TEM and c corresponding electron energy loss spectroscopy (EELS) spectrum of the tribofilm area in (a). The inset in (b) is the lattice fringe spacing obtained from the red row. d Scanning transmission electron microscopy (STEM) image, and corresponding e energy-dispersive X-ray spectroscopy (EDS) line scanning, f–h elemental mapping images of the cross-sectional tribofilm formed by 5 wt% DOM. i High-angle annular dark-field STEM (HAADF-STEM) image, and j corresponding EDS elemental concentration table of the tribofilm area in (a). The red circles in Fig. 4i represent typical iron single atoms. k Fourier transformation (FT) of k³-weighted extended X-ray absorption fine structure (EXAFS) spectra of Fe foil, Fe₂O₃, Fe₃O₄, and the tribofilm formed by 5 wt% DOM. l Wavelet transforms (WTs) for the k³-weighted EXAFS signals from the tribofilm formed by 5 wt% DOM. Source data are provided as a Source Data file.

The effect of molecular structure on mechanochemistry

The above experiments demonstrate a better tribological performance for DOM than other additives tested, which is attribute to a tribofilm formation composed of graphitic carbon. This tribofilm formation can be ascribed to the much stronger adsorption of DOM on steel surfaces compared to other additives such as octanol, as well as the increased chemical reactivity of DOM to steel surfaces. These attributes can be demonstrated further by the quartz crystal microbalance with dissipation monitoring (QCM-D, Supplementary Figs. 25, 26), and the energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) calculated by first principles (Supplementary Fig. 27). The strongly adsorbed DOM film plays a dual role in enhancing tribological performance. First, it physically separates the solid-solid contact during rubbing, thereby reducing friction and wear. Second, it ensures a sufficient supply of DOM molecules at the friction interface to participate in tribochemical reactions, facilitating the formation of a graphitic carbon tribofilm. The initial formation of this tribofilm depends on an adequate concentration of reactive species to initiate the reaction. If the concentration is too low, the tribofilm formation rate will be limited. Furthermore, the tribofilm formation is a dynamic process involving simultaneous formation and removal. Insufficient additive adsorption results in the removal rate exceeding the formation rate, preventing tribofilm accumulation. Therefore, the strong adsorption of DOM on the steel surface ensures a consistent supply of reactants, balancing the dynamic formation process and enabling graphitic carbon tribofilm formation. This enhanced adsorption is a key factor in DOM’s tribological performance.

Note that while there are several studies addressing the formation of graphite-like carbon films, they often involve specific conditions such as noble metal substrates⁵⁵, which are cost-prohibitive, anaerobic environments⁵⁶, requiring complex sealing systems, or water-based lubricants⁵⁷, which are less applicable to many industrial applications. In contrast, this work demonstrates that the green additive DOM can effectively form a graphitic carbon layer on engineering steel surfaces, a material widely used in industry. Additionally, the correlation between graphitic carbon formation and molecular structures remains poorly understood due to the challenges in elucidating the reaction pathways during complicated tribochemical reactions. Therefore, it is of great significance to investigate the molecular structure effect on graphitic carbon formation and the corresponding tribological performances.

Typically, the tribochemical reaction of graphitic carbon formation can be initiated by the free radicals^58,59, which were easily generated during the rubbing process^60,61. Therefore, this sheds light on the main question raised by this work, i.e., which bond(s) in DOM dissociate first, consequently leading to the formation of the free radicals that initiate the graphitic carbon film formation process? In the case of DOM, considering the lower dissociative energy of the C-C bond compared to the C-H bond, the C-C bond might be more readily dissociated, thus forming free radicals that initiate the tribochemical reactions. Meanwhile, the dissociative energy of one chemical bond can also be influenced by the adjacent groups since these groups affect the stability of generated free radicals through the lone pair effect and/or hyperconjugation effect⁶². Therefore, it is conceivable that the C-C bond between the hydroxyl-bonded carbon and ester group carbon is the easiest to dissociate, leading to the formation of free radicals as shown in Fig. 5.

Fig. 5: The proposed reaction mechanism of DOM during friction.

The two arrows suggest the position where the first bond is to be dissociated, and the red oxygen atoms suggest the position that can stabilize the free radical through the lone pair effect.

It is noted that the oxygen from both the hydroxyl side and ester side (the above red atoms) have two lone pairs of electrons which can donate electron density to the half-empty p orbital of carbon radicals. Since carbon radicals are electron deficient species, the electron-donating effect from lone pair electrons help to stabilize them, known as the lone pair effect⁶². As a result, the stabilized free radicals can further propagate the tribochemical reactions to form the graphitic carbon⁵⁸. To verify this point further, the tribological properties of diester with different chain lengths (Table 1) but similar structure to DOM have been investigated, as shown in Fig. 6. The tribological tests of diesters including dioctyl malonate (DOT), dioctyl fumarate (DOF), dioctyl adipate (DOA), dioctyl sebacate (DOS), didodecyl succinate (DOSN) were all carried out under 36 N at 30 °C.

Table 1 The molecular structure of diesters derived from different lengths of carboxylic acids (n_c) and different lengths of alcohols (n_a), including dioctyl malonate (DOT), dioctyl fumarate (DOF), dioctyl adipate (DOA), dioctyl sebacate (DOS), didodecyl succinate (DOSN)

Fig. 6: Tribological performance and surface analysis on wear track of additives with different chain lengths.

a Average friction coefficient and b wear track of different diesters. c The correlation between the Young’s modulus of the island area on the wear track and their tribological performances. The error bars in (a–c) represent the standard deviation based on triplicate measurements. d magnified optical image of wear track after rinsing, e Raman spectra on wear track, f Raman G band mapping image, g carbon, h oxygen, i iron X-ray photoelectron spectroscopy (XPS) depth analysis on wear track formed by additives with different chain lengths. j The proposed free radical generation mechanism of dioctyl malonate (DOT) and dioctyl sebacate (DOS) during friction, and the red oxygen atoms suggests the position that can potentially stabilize the free radical through lone pair effect. The scale bars in (d)–(f) are 25 µm. Source data are provided as a Source Data file.

The diester derived from short-chain carboxylic acid (DOT, DOF in Fig. 6a, b, Supplementary Figs. 28, 29) exhibits lower friction (0.12–0.13) and wear (210 µm) compared to that from long-chain carboxylic acid (DOA, DOS in Fig. 6a, b, Supplementary Figs. 28, 29). Moreover, a distinctive gray island tribofilm, composed of graphitic carbon with a low Young’s modulus, is observed on wear track formed by diesters derived from short-chain carboxylic acid (DOT, DOF, Fig. 6d–g, Supplementary Figs. 30–34), a feature not present on the diesters derived from long-chain carboxylic acid (DOA, DOS). Note that the low friction coefficient and wear track width are usually accompanied with the formation of gray island tribofilm with low Young’s modulus (Fig. 6c), further implying that this carbon film contributes to the tribological performance at macro scale. In addition, the diester derived from short-chain carboxylic acid but long-chain alcohol can also provide low friction, wear, and graphitic carbon formation (DOSN in Fig. 6). Therefore, it can be proposed that for diester derived from short-chain carboxylic acids, the free radicals generated on both sides after C-C bond dissociation can be stabilized by the oxygen from each side of the dissociated bond through lone pair effect (indicated by red oxygen atoms in DOT, Fig. 6j). This stabilization facilitates the initiation of tribochemical reactions. In contrast, for diesters derived from long-chain carboxylic acids, only one side of the generated free radicals can be stabilized by the oxygen from the ester group (DOS, Fig. 6j). The other side is unable to achieve stabilization due to the significant distance between free radicals and oxygen atom, resulting in a high dissociation energy that impedes the effective initiation of reactions. Hence, it can be concluded that the free radicals stabilized by lone pair effect contribute to lower bond dissociation energy, thereby triggering tribochemical reactions that lead to the formation of graphitic carbon and the reduction of friction and wear.

The effect of tribopairs on mechanochemistry

The chemistry of rubbing surfaces can have a strong influence on the formation of tribofilms. When both the top balls and bottom discs were made of Si₃N₄ (Supplementary Fig. 35a, b), sapphire (Supplementary Fig. 35c, d), glass (Supplementary Fig. 35e), or Diamond-like Carbon coated steel (DLC) (Supplementary Fig. 35f), 5 wt% DOM in PAO could not reduce friction. Nevertheless, once the bottom disc specimen is replaced by steel, 5 wt% DOM showed considerably lower friction and wear (Fig. 6a, b), and a graphitic carbon tribofilm was formed once again on the steel surface (Raman in Fig. 7a, b). This suggests that steel (or iron in steel) is an essential requirement for graphitic carbon formation, which might be attributed to its catalytic effects⁶³. Considering that the catalysis process is an interfacial phenomenon that occurs at the solid-liquid interface, once a tribofilm with a thickness of a few nanometers covers the steel surface, it prevents the interaction between the metallic tribopair surface and liquid lubricant (Fig. 7c); hence, it cannot grow to a thickness of about 30 nm. Nevertheless, in this study, the iron single atoms observed in TEM (red circles in Fig. 4i) were in-situ generated during the rubbing process and were then incorporated into the graphitic carbon tribofilm (Fig. 7d). Consequently, the iron single-atom catalyst found in tribofilm can maintain the solid-liquid interaction with DOM molecules and therefore continuously catalyze them to produce graphitic carbon tribofilm to a thickness of 30 nm (Figs. 4a, 7e). The remarkable catalytic performance of Fe single atoms has been demonstrated in facilitating C–H and C–C bond dissociation^53,64, both of which are critical steps in the formation of graphitic carbon. This performance arises from the atomic dispersion of active catalytic centers and their distinctive electronic structure.

Fig. 7: Tribological performance of polyalphaolefin (PAO) containing 5 wt% dioctyl malate (DOM) effect on various surfaces.

Friction coefficient and wear track images, and Raman spectra of PAO and 5 wt% DOM in PAO for (a) Diamond-like carbon-coated steel (DLC) ball-on-steel disc under 24 N and b glass ball on steel disc under 36 N. The schematic of (c) the blocked interaction between DOM and steel surface with no iron single atoms formation, d the interaction between DOM and iron single atoms distributed on a thin carbon film, and e a thick carbon film formed on steel surface under iron single atoms catalysis. Source data are provided as a Source Data file.

To further elucidate the impact of Fe single atoms on the conversion of DOM into graphitic carbon tribofilms, the activation energy for C–C bond dissociation in simplified DOM on iron single-atom surfaces, iron cluster, and Fe (110) surface was respectively calculated using DFT simulation (Supplementary Fig. 36). The results reveal that the activation energy for C–C bond dissociation is significantly reduced to 1.08 eV on iron single-atom surfaces, which is notably lower than that on iron clusters (1.41 eV) and Fe (110) surface (1.66 eV). This underscores the catalytic efficiency of single iron atoms in activating DOM, which facilitates the subsequent formation of graphitic carbon. Note that although the graphitization process typically requires high temperatures of up to 3000 °C⁶⁵, far exceeding the 30 °C condition of our friction tests, the localized temperature at single asperities can be one to two orders of magnitude higher than the bulk liquid temperature⁶⁶, especially under boundary lubrication. This elevated temperature is sufficient to induce partial graphitization⁶⁷. Meanwhile, the high contact pressure and shear stress generated during friction can further facilitate tribofilm formation through mechanochemical processes^68,69.

To elucidate the atomistic mechanism governing the tribofilm formation on various surfaces, ReaxFF reactive molecular dynamics simulations were conducted with initial configurations comprising DOM molecules sandwiched between sliding tribological interfaces (see Supplementary Fig. S37). While the thickness of the liquid film was around 2 nm at the beginning of the simulation (Fig. 8a), it reduced to around 1 nm by the end of simulation (Supplementary Fig. 38), which closely matches the liquid film thickness calculated using Dowson and Hamrock’s equation (Supplementary Table 2). Note that previous studies have shown that boundary lubrication does not imply the complete absence of confined lubricants. Instead, the tribopair surfaces may still be separated by a thin molecular film, typically ranging from one to a few nanometers depending on the $\lambda$, which is the ratio between the thickness of the lubricating liquid film and the combined surface roughness of the two tribopair surfaces⁷⁰. Notably, the release of hydrogen atoms from the DOM molecules on the Fe (110) surface was observed at the beginning of the simulation (Fig. 8b). Remarkably, more than 80% of the C-H bonds dissociate within 1200 ps, as depicted in Fig. 8d. Consequently, most of the released hydrogen atoms recombine to form H₂ molecules, as illustrated in Fig. 8e. As a result, multi-membered carbon rings gradually form on the iron surface (Fig. 8c, f), eventually leading to the reconstruction of a large-scale defective or disordered graphene-like structures^71,72. In contrast, the dehydrogenation of DOM on the SiO₂ (001) surface occurs at a significantly lower rate (<15% within 1.25 ns, Fig. 8d), resulting in no/little H₂ and multi-membered carbon rings formation (Fig. 8e, f, Supplementary Fig. 39), which is consistent with the experimental results on glass discs surfaces (Supplementary Fig. S35e). Thus, the atoms on the steel surface, as catalysts, expedite the dehydrogenation process of DOM, thus facilitating the formation of graphitic carbon.

Fig. 8: Schematic of the structural evolution of the dioctyl malate (DOM) molecules confined between two Fe (100) surfaces.

a DOM molecules confined between two Fe (100) surfaces at 0 ps; b, c The top view of DOM on Fe (100) surface at different times. The surface is from the dashed black box in Fig. 8a. The number of d C-H bonds, e H-H bonds and f carbon rings, throughout the simulation where the DOM molecules are confined between two Fe (110) and SiO₂ (001) surfaces. Source data are provided as a Source Data file.

Containing no heavy metal or sulfur and phosphorus, the diesters in this work, typically DOM, are green and highly effective anti-friction and anti-wear additives under extreme loading conditions and in ultra-low viscosity oils, PAO2. Compared to neat PAO2, DOM demonstrates exceptional tribological performance by reducing friction by up to 50% and wear by as much as 80%. Moreover, it outperforms conventional additives, such as octanol, oleic acid, GMO, and ZDDP, which have been widely employed in the industry for decades. Its tribological performance is attributed to the in-situ formation of a graphitic carbon tribofilm on rubbing steel surfaces. This tribofilm, with a low Young’s modulus and shear strength, prevents direct metal-to-metal contact hence reducing friction and wear. This tribofilm tends to form from diesters derived from short-chain carboxylic acid due to their lone pair effect, which stabilizes the carbon free radicals. Furthermore, this graphitic tribofilm can only form on steel surfaces, suggesting that the catalytic reactivity of the iron single atoms is essential for its continuous generation during sliding. This concept shown here provides a strategy for the design of effective and sustainable anti-friction and anti-wear additives (like DOM) for future tribological systems in industrial applications.

Methods

Materials

PAO with a viscosity of 5.3 mPa.s at 30 °C was used as base oil as received from Chevron Corporation. Octanol (≥99%), malic acid (99%), oleic acid (OA, ≥99%), and hexane (anhydrous, 95%) were all purchased from Sigma-Aldrich, and they were used without further purification. A primary C8 ZDDP (≥90%) was purchased from Wuhan Yuancheng Technology Co., Ltd. Dioctyl malate (DOM) was synthesized using previously described method^73,74. Specifically, a mixture of 68.6 g of octyl alcohol and 3.0 g of p-toluene sulfonic acid was dissolved in 100 mL of toluene under magnetic stirring. Subsequently, 30.0 g of malic acid was added to the flask with continuous stirring. The reaction was carried out under azeotropic distillation with toluene to remove the water produced. After 3 h, the toluene was removed under reduced pressure (30 torr). The crude product was extracted with ethyl acetate and washed three times with water, followed by neutralization with a saturated NaHCO₃ solution. The organic layer was separated using a separatory funnel, dried over MgSO₄, and filtered. The solvent was evaporated, and the residue was distilled under reduced pressure (~55 mTorr) to remove excess octyl alcohol. The final product, dioctyl malate, was obtained as a yellowish oily liquid. The chemical structure of DOM was determined by ¹H and ¹³C NMR spectra, as shown in Supplementary Fig. 40 and Supplementary Fig. 41. ¹H NMR (400 MHz, CDCl₃) δ [ppm] = 4.45 (t, J = 8.0 Hz,1H), 4.17 (m, 2H), 4.07 (t, J = 8.0 Hz, 2H), 2.79 (m, 2H), 1.61 (m, 4H), 1.36–1.16 (d, J = 12.0 Hz, 20H), 0.90–0.87 (t, J = 8.0 Hz, 6H). ¹³C NMR (400 MHz, CDCl₃): δ [ppm] 173.5, 170.6, 67.4, 66.2, 65.2, 38.8, 31.8, 29.2, 28.6, 25.9, 22.7, 14.1. DOT, DOF, DOA, DOS, DOSN were all purchased from Sichuan Yuanqi Pharmaceutical Technology Co., Ltd., and were used as received. 5% octanol, 5% oleic acid, 5% ZDDP, and 5% DOM in PAO were prepared by stirring at room temperature for 15 min.

Tribological test

Tribological tests were performed using an SRV4 tribometer (Optimol Instruments). Specifically, the low disc was stationary, whereas the top ball is moving against the disc with a reciprocating mode. The diameter of the balls was 10 mm, whereas the diameter of the disc was 24 mm, with a thickness of 7.88 mm. The Balls and discs were composed of different materials, including AISI 52100 steel, DLC-coated steel, Si₃N₄, sapphire, and glass, all of which were purchased from Beijing Jingyue Hongbo Technology Co., Ltd. The surface roughness (Ra) of the balls and discs was ~10 nm, and their mechanical properties can be found in Supplementary Table 3. Prior to the friction test, all the samples were ultrasonically rinsed in a mixture of ethanol and petroleum ether (v/v = 1:1), followed by drying in air overnight. The friction test of neat PAO, 5% DOM, 5% octanol, 5% OA, and 5% ZDDP were conducted at 30 °C under 36 N. The reciprocating frequency was 10 Hz with a stoke length of 1 mm. The elastohydrodynamic film thickness of various additives in PAO was calculated according to Dowson and Hamrock’s equation (Note S1), and it was approximately 1.39 nm for the friction test with a frequency of 10 Hz at 30 °C. The λ, which is the ratio of calculated liquid film thickness to initial root mean square roughness of the two surfaces (Rq, nm), was used to evaluate the lubrication regime, and it was approximately 0.1. Thus, friction tests with various additives were all performed under boundary lubrication. The tribological performance was also evaluated on different tribopair surfaces under loads of 12, 24, and 36 N, and their corresponding contact pressure is listed in Supplementary Table 1. All friction tests were repeated three times, and all showed good reproducibility. The wear track surface was rinsed by hexane before surface analysis. The wear volume (V) was calculated with the following equation,

$$V=\left(\frac{\pi h}{6}\right)\left(\frac{3{d}^{2}}{4}+{h}^{2}\right)$$

(1)

Where d is the wear scar diameter, r is the radius of the ball, and

$$h=r-\sqrt{{r}^{2}-\frac{{d}^{2}}{4}}$$

(2)

Surface analysis

The viscosity of lubricants at 30 °C was tested by rheometer (MCR02, Anton Paar) at shear rates from 10 to 3000 s⁻¹, as shown in Supplementary Fig. 42. The three-dimensional topography of the wear track was determined by white-light interferometry (ZYGO Lambda, USA). The topography and nanomechanics of the wear track were investigated by AFM (MFP-3D, Asylum Research) under the contact mode. The AFM tip was composed of silicon with a spring constant of 0.29 N/m after calibration, and its free resonant frequency was 13 kHz. The lateral detector sensitivity was 25.66 nN/mV, which was calibrated by improved wedge method⁷⁵. The topography of the wear track in Supplementary Fig. 16 was obtained under a deflection setpoint of 0.5 V. Additionally, to assess the robustness of the tribofilm on wear track, a repeated friction test was applied 110 times on a 10 μm × 10 μm rectangular box inside the tribofilm (Supplementary Fig. 17, 18). The deflection setpoint was 8 V during the test, and the topography and lateral force were recorded for each friction test (Fig. 2d). The force–distance curves were obtained via AFM in three areas: the island-like area inside the wear track, no-island area inside the wear track, and unrubbed area. Specifically, the AFM tip approached the sample surface and then retracted from it, during which the force and distance between the AFM tip and sample surface were recorded (Supplementary Fig. 19). The maximum pull-off force during AFM retraction from the surface was used to evaluate the adhesion of the AFM tip to the sample surface (Fig. 2e). Force–distance curves were collected at 100 points in each area. The Young’s modulus and hardness of the tribofilm was evaluated by a nanoindentation test (Bruker TI 980 triboindenter). Specifically, a tip composed of a diamond with a diameter of 30 nm gradually approached the sample surface and reached a depth of 40 nm within the first 5 s. After that, the tip was maintained in the same position for 5 s, and then retracted from the sample surface. The force was monitored during the entire process, and Young’s modulus and hardness were fitted using Oliver–Pharr model. Raman spectra (LabRAM HR Evolution, Horiba) with an excitation wavelength of 532 nm were obtained on the wear track to determine its chemical composition. The Raman spectra were collected at a power of 5 mW and acquisition time of 30 s. The Raman mapping image was collected in a 150 μm × 115 μm area inside the wear track with an acquisition step size of 3 μm. Micro-FTIR (Vertex 70 V, Bruker) was performed on an 80 μm × 80 μm rectangular box on the wear track, and the background of CO₂ was removed during data process. A lamellar layer on the wear track formed by 5% DOM in PAO was prepared via FIB (LYRA3, TESCAN. Q.S., Czech Republic). Subsequently, the cross-sectional morphology and elemental mapping distributions were observed by TEM (JEM 2100 F, Japan, 200 kV) and EDS. Prior to sample preparation, chromium and platinum layers were deposited on the sample surface using a precision etching and coating system (Gatan 682) to protect the sample. The elemental compositions and specific chemical statuses at various depths were determined by XPS (Ulvac-Phi Quantera II, Japan). Each XPS test was run on a 100 μm × 100 μm rectangular box, and the sputter tests were performed at a rate of 0.3 nm/s. This sputtering rate was referred to as the SiO₂ substrate. The XPS spectra were calibrated using sp³ C 1s as the reference at 284.8 eV. The wear track surface lubricated by 5% DOM in PAO was further investigated by X-ray absorption spectroscopy under the fluorescence mode to reveal the chemical state of iron. The test was conducted on the BL14W beamline using Si (111) crystal monochromators at the Shanghai Synchrotron Radiation Facility, and the XAFS spectra were collected at room temperature using a 4-channel Silicon Drift Detector Bruker 5040. Iron foil, FeO, and Fe₂O₃ tested in the transmission mode were used as reference samples in this study. The EXAFS fitting parameters can be found in Supplementary Table 4.

The adsorption of additives on tribopair surface was investigated by QCM-D (Biolin Scientific). The sensor was composed of a Fe₂O₃-coated quartz with a fundamental frequency of 5 MHz. Prior to the test, the sensor was ultrasonically cleaned in ethanol for 30 min, followed by UV ozone irradiation for 30 min. The solution was pulled into the sensor cell by a pump with flow rate of 100 μL/min. The pipes were made of polytetrafluoroethylene, whereas the O-ring and gasket for sealing were made of Kalrez, which was chemically stable in the solution in this work. The resonance frequency at overtone n = 1, 3, 5, 7, 9, 11, and 13 was recorded. A baseline was first obtained by neat PAO, followed by the introduction of 5% octanol/DOM in PAO. Subsequently, neat PAO was pumped into the sensor cell again to flush the sensor surface. The temperature was maintained at 30 °C during the test, and the resonance frequency was monitored during the entire process. The resonance frequency shift due to liquid loading, which arose from the viscosity and density difference of different liquids, was corrected in this work according to the method in the literature^76,77,78. Hence, the adsorbed mass ($\triangle m$) can be calculated by the following formula:

$$\Delta m=-\frac{C{f}_{n}}{n}$$

(3)

where C is a constant with a value of 17.7 ng/(cm². Hz), n is the harmonic overtone number, and ${f}_{n}$ is the frequency of each overtone after the viscosity correction. Because different overtones presented the same resonance frequency, n = 3 was used in this study.

The dissociation energy of the C-C bond in simplified DOM on different surfaces

Density functional theory (DFT) simulation was conducted to calculate the dissociation energy of C-C bond in simplified DOM on different surfaces, including Fe single atoms, Fe cluster, and Fe (110) surface. For the model of Fe single atom and Fe cluster, a supercell containing a 5 × 3 graphene sheet was used to build the carbon support, in which the defect of a single C atom with three coordination oxygen atoms was constructed (Supplementary Fig. 36). And then, Fe single atom and Fe₄ cluster were loaded to form Fe1/O-G (Fe single atom) and Fe4/O-G models (Fe cluster). Meanwhile, periodic slabs with (4 × 4) surface unit cells were applied to model the Fe (110) surfaces, and the bottom two layers were fixed during structural optimizations while other layers were fully relaxed. The models of simplified DOM on different surfaces are provided in Supplementary Data 1.

All the first-principles spin-polarized calculations were performed by using the Vienna ab initio Simulation Program^79,80. The generalized gradient approximation (GGA) in the Perdew–Burke–Ernzerhof form and cutoff energy of 500 eV for planewave basis set were adopted⁸¹. A 2 × 2 × 1 Monkhorst-Pack⁸² k grid was used for sampling the Brillouin zones at structure calculation. The ion-electron interactions were described by the projector augmented wave (PAW) method⁸³ [5]. The convergence criteria of structure optimization were chosen as the maximum force on each atom less than 0.02 eV/Ǻ with an energy change less than 1 × 10⁻⁵ eV. To calculate the kinetic energy barrier of chemical reactions, the climbing image nudged elastic band method was used to search for the transition states⁸⁴.

HOMO-LUMO calculation

The energy gap between HOMO and LUMO was calculated using DFT with the method of BLYP/GGA and DNP as the base set⁸⁵.

ReaxFF reactive simulation setup

ReaxFF reactive molecular dynamics (MD) simulations were conducted to elucidate the lubrication mechanism of DOM on different surfaces. The Fe (110) and SiO₂ (001) surfaces were constructed to model the steel and glass surfaces in experiments, as their surface energies are the lowest^86,87. All ReaxFF MD simulations were executed using the LAMMPS package⁸⁸ within a canonical ensemble (NVT) framework, employing a time step of 0.25 fs. In all simulations, we adopted a force-biased Monte Carlo (fbMC) technique⁸⁹ to accelerate the tribochemical reaction, i.e., 50,000 MC steps every 25 ps of MD steps.

Our typical computational model consists of two slabs of either Fe or SiO₂, separated by a vertical distance of 80 Å, as depicted in Supplementary Fig. 37. The initial simulation box dimensions are ~28.6 Å × 28.3 Å × 130.0 Å for the Fe (110) surface and 25.5 Å × 24.5 Å × 128.0 Å for the SiO₂ surface. Periodic boundary conditions were applied in both the x and y directions. Within this setup, 36 lubricating DOM molecules are randomly placed in the vacant space between the two slabs, constituting a total of 720 carbon atoms. As shown in Supplementary Fig. 37, the simulated model comprises five layers, ordered from bottom to top as follows: (1) the stationary bottom rigid-body layer of Fe or SiO₂ substrate atoms (2) a free Fe or SiO₂ substrate layer where atoms exhibit dynamic movement in the simulations, (3) DOM molecules positioned between the two slabs, (4) another free Fe or SiO₂ layer with atoms allowed to move dynamically in the simulations, and (5) the top rigid-body layer of Fe or SiO₂, which is laterally movable. With this initial configuration, three steps were carried out to imitate the tribological process: (1) equilibration of the system at room temperature for 20 ps. (2) loading a pressure of 0.5 GPa on the top rigid-body layer along the z-direction while maintaining the bottom rigid-body layer fixed in space, followed by equilibration of the compressed system for 100 ps, and (3) sliding of the top layer along the x-direction at a constant velocity of 0.3 m/s under the applied load for 1.25 ns while the bottom rigid-body layer remains fixed. During the sliding, the system is equilibrated at 1600 K using the Nosé-Hoover thermostat to accelerate the tribochemical reactions. Additionally, it’s worth noting that local areas on a single asperity may attain elevated temperatures during the rubbing process, as previously discussed^90,91.

In this study, the ReaxFF parameters governing SiO₂-hydrocarbon interactions were adopted from the Protein/Silica/CuOx force field, which was used to study the chemical mechanical polishing process successfully⁹². Regarding the Fe-C/H/O interaction, we merged the C/H/Fe⁹³, Fe/C/O/H⁹⁴, and C/H/N/O/S⁹⁵ force fields to study the graphene growth in Fe nanocluster. The molecular dynamics trajectories and ReaxFF force field parameters are provided in Supplementary Data 2.

C/O/H/Fe-2023 ReaxFF force field development and validation

The ReaxFF reactive force field developed by van Duin et al. ⁹⁶ is a bond-order-dependent force field, which is known to describe formation and dissociation of chemical bonds well. It determines the connectivity between every pair of atoms using bond-order calculations based on interatomic distances that are updated at every molecule dynamics time step. The potential can be expressed by the following⁹⁷:

$${E}_{{system}}={E}_{{bond}}+{E}_{{angle}}+{E}_{{tors}}+{E}_{{over}}+{E}_{{vdw}}+{E}_{{coul}}+{E}_{{specific}}$$

(4)

in which ${E}_{{bond}}$, ${E}_{{angle}}$, ${E}_{{tors}}$ and ${E}_{{over}}$ are two-body, three-body and four-body contributions, respectively, and all of those terms are bond-order dependent. The bond order ${BOij}$ between a pair of atoms can be obtained directly from the interatomic distance ${rij}$ as given in Eq. 5:

$${{BO}}_{{ij}} = {{BO}}_{{ij}}^{\sigma }+{{BO}}_{{ij}}^{\pi }+{{BO}}_{{ij}}^{\pi \pi }\\ =+\exp \left[{p}_{{bo}3}{\left(\frac{{r}_{{ij}}}{{r}_{0}^{\pi }}\right)}^{{p}_{{bo}4}}\right]+\exp \left[{p}_{{bo}5}{\left(\frac{{r}_{{ij}}}{{r}_{0}^{\pi \pi }}\right)}^{{p}_{{bo}6}}\right]$$

(5)

where ${BOij}$ is the total bond-order between two atoms $i$ and $j$, ${r}_{{ij}}$ is the inter-atomic distance, ${r}_{0}$ are the equilibrium bond distances of the $\sigma,$ $\pi$ and $\pi \pi$ bonds, and ${p}_{{bo}1}$ to ${p}_{{bo}6}$ are empirical parameters.

The ${E}_{{vdw}}$ and ${E}_{{coul}}$ are dispersive and electrostatic contributions between all atoms, regardless of connectivity and bond-order. ${E}_{{specific}}$ represents specific terms that are not included generally. Such a general formalism enables ReaxFF to accurately capture covalent, ionic, and metallic bonding, as well as transition states along a reaction pathway, it has been used successfully for a wide range of material systems, including metals, metal-oxides, ceramics, metal organics, and hydrocarbons. The details of ReaxFF potential can be found in the CHO_2008 publication⁹⁸.

Since the C/H/N/O/S force field effectively describes graphitic carbon and hydrocarbon molecules, in this study, our primary focus centered on establishing pair potentials for Fe-C and Fe-H interactions. To achieve this, we retrained the bond terms, such as Fe-C and Fe-H, as well as the bond-angle terms for C–C–Fe, C–Fe–C, Fe-C-Fe, C-Fe-Fe, H-C-Fe, H-Fe-H, Fe-Fe-H, O-C-Fe angles. This optimization process was carried out using the successive one-parameter search technique implemented in the ReaxFF standalone code. In our training set, the binding energy of carbon atoms on Fe (110) was considered. The ReaxFF predictions for binding energies of 5.77 in bridge sites and 7.11 eV in hollow sites of Fe (110) surface, reasonably align with the DFT calculations (6.72 and 8.19 eV, respectively). Furthermore, the heat formation energies of FeC, Fe₂C, and Fe₃C predicted by ReaxFF are 2.12, 0.39, and 0.26 eV, respectively, which closely match the DFT calculations (1.91, 0.56, and 0.17 eV, respectively). We also incorporated the equation of state of Fe₃C to describe the FeC crystal. Additionally, we considered the dehydrogenated catalytic reaction of the CH₄ modeling molecule on the Fe (110) surface during our training. The DFT reaction barrier is 1.00 eV and ReaxFF predicts a barrier of 0.65 eV. It is evident that all the data in our training set effectively capture the interaction between the Fe surface and graphitic carbon. In summary, our ReaxFF results exhibit agreement with DFT data, validating the accuracy of ReaxFF in this study.

To emulate the loss of H₂ molecules following dehydrogenation/chain scission, an efficient H₂ removal scheme was implemented. By extracting information from the atomic connection table generated by LAMMPS using the “reaxff/bonds” keywords, the atom id of H in H₂ molecule can be identified and then removed from the simulation box. Similarly, the count of C-H bonds was determined. Specifically, we monitored the numbers of H₂ molecules and C-H bonds every 25 ps MD steps with 50,000 MC steps (Note, we verified that increasing the monitoring frequency did not significantly affect the results). The temporal evolution of the number of C-H bonds, H₂ molecule,s and multi-membered carbon rings for both Fe (110) and SiO₂ (001) surfaces is illustrated in Fig. 8d–f.