Molecules with a TEMPO-based head group as high-performance organic friction modifiers

High-performance organic friction modifiers (OFMs) added to lubricating oils are crucial for reducing energy loss and carbon footprint. To establish a new class of OFMs, we measured the friction and wear properties of N-(2,2,6,6-tetramethyl-1-oxyl-4-piperidinyl)dodecaneamide referred to as C12Amide-TEMPO. The effect of its head group chemistry, which is characterized by a rigid six-membered ring sandwiched by an amide group and a terminal free oxygen radical, was also investigated with both experiments and quantum mechanical (QM) calculations. The measurement results show that C12Amide-TEMPO outperforms the conventional OFMs of glyceryl monooleate (GMO) and stearic acid, particularly for load-carrying capacity, wear reduction, and stability of friction over time. The friction and wear reduction effect of C12Amide-TEMPO is also greatly superior to those of C12Ester-TEMPO and C12Amino-TEMPO, in which ester and amino groups replace the amide group, highlighting the critical role of the amide group. The QM calculation results suggest that, in contrast to C12Ester-TEMPO, C12Amino-TEMPO, and the conventional OFMs of GMO and stearic acid, C12Amide-TEMPO can form effective boundary films on iron oxide surfaces with a unique double-layer structure: a strong surface adsorption layer owing to the chemical interactions of the amide oxygen and free radical with iron oxide surfaces, and an upper layer owing to the interlayer hydrogen-bonding between the amide hydrogen and free radical or between the amide hydrogen and oxygen. Moreover, the intralayer hydrogen-bonding in each of the two layers is also possible. We suggest that in addition to strong surface adsorption, the interlayer and intralayer hydrogen-bonding also increases the strength of the boundary films by enhancing the cohesion strength, thereby resulting in the high tribological performance of C12Amide-TEMPO. The findings in this study are expected to provide new hints for the optimal molecular design of OFMs.


Introduction
Friction and wear at moving parts of machines are estimated to consume 23% of the total energy of the world [1]. Therefore, reducing friction and wear to the lowest possible level is crucial for reducing energy loss and carbon footprint. One cost-effective solution is to use lubricating oils of low viscosity with a small amount of friction modifier additives [2,3]. Low viscosity is desirable because it leads to low shear resistance between rubbing surfaces intermediated with lubricating oils in the hydrodynamic lubrication regime [2,4,5]. As the sliding velocity decreases or the normal load increases, however, low-viscosity oils are difficult to intervene between rubbing surfaces, causing an undesirable shift from the hydrodynamic to boundary lubrication regime. In the boundary lubrication regime, direct solid-solid contacts are likely to occur, thereby resulting in high friction, severe wear, or even catastrophic system failure. This problem can be solved by the addition of friction modifiers which form boundary films on the rubbing surfaces, and thus prevent direct solid-solid contacts [2,3,[6][7][8][9][10]. Friction modifier additives not only directly improve the boundary lubrication performance, but also allow the use of low-viscosity lubricating oils, and thus indirectly improve the hydrodynamic lubrication performance. Due to the urgent need for environmental protection, there is an increasing demand for shifting from the currently used sulfur and/or phosphoruscontaining additives toward ashless organic friction modifier (OFM) additives that are exclusively composed of carbon, hydrogen, oxygen, and nitrogen atoms [2,3,[11][12][13][14]. Although OFMs have been extensively studied dating back over a century [15,16], further improvement of the friction and wear reducing performance still remains challenging.
OFMs are usually amphiphiles with a nonpolar hydrocarbon tail group attached to a polar head group [2,3,17]. It is generally accepted that OFMs form boundary films with the polar head group adsorbed on solid surfaces and the nonpolar tail group aligned outward into the base oil [2,[18][19][20][21]. The design of the head group, which determines the surface adsorption ability of OFMs, and thus load-carrying capacity and durability of the boundary films, is a key issue to improve the performance of OFMs [2,[22][23][24]. The design factors include the number and type of functional groups in the head group. For the OFMs developed so far, single or multiple functional groups of carboxyl, alcohol, amine, amide, imide, and ester have been used [2,3,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. Studies showed that carboxyl and amine groups generally work better than alcohol, ester, and nitrile groups [2,25]. For instance, Onumata et al. [26] reported that oleic acid exhibited higher effect of friction reduction than oleyl alcohol at steel-steel contacts. Cyriac et al. [27] found that stearamine required less time to form adsorption films on steel surfaces and exhibited lower friction coefficients than OFMs based on amide and carboxyl groups. Fry et al. [28] also showed that octadecylamine exhibited good friction-reducing performance, particularly at the initial stage.
Compared with a single functional group, multiple functional groups can enhance the adsorption strength through multi-site adsorption or chelate effect. Although it has long been considered that multiple functional groups might lower the packing density of the adsorbed molecules due to the relatively large size of the head group [2], recent studies suggested that complete surface coverage was neither practically achievable nor necessary for effective friction reduction [28,40]. Glyceryl monooleate (GMO), which contains two alcohol groups and one ester group and is one of the most widely employed OFMs [24], was found to give lower friction and wear on steel surfaces than OFMs with a single carboxyl or amine groups [29]. It was also reported that GMO exhibited ultralow friction for rubbing surfaces of tetrahedral amorphous diamond-like carbon (DLC) [2,30]. Kuwahara et al. [31] found that glycerol, which contained three alcohol groups, also led to ultralow friction with negligible wear on DLC surfaces. Nalam et al. [33] studied the effect of fatty amines with multiple amine groups and found that the adsorbed masses increased with the number of amine groups, while the adsorption kinetics decreased. Hu et al. [34] synthesized a series of OFMs with multiple amine groups and suggested the number of nitrogen atoms and the slim molecular configuration as the main factors affecting the tribological properties. Desanker et al. [36,37] developed a new type of OFM containing a nitrogen heterocycle with four nitrogen centers and demonstrated its excellent performance in friction and wear reduction. For this new type of OFM, He et al. [38] reported that the increased surface adsorption energy owing to the chelate effect was an essential reason for the increased stability and durability of the surface adsorbed films and thus the excellent boundary lubrication performance, as compared with OFMs with a single amine group.
In contrast, we have proposed N-(2,2,6,6-tetramethyl-1-oxyl-4-piperidinyl)dodecaneamide, which is referred to as C 12 Amide-TEMPO, as a new class of OFM in our previous study [25]. Its head group is characterized by a rigid six-membered ring with a free radical at the terminal and an amide group at the opposite side, as seen from Fig. 1(a). Although TEMPO (i.e., the six-membered ring with a free radical) and its derivatives with a hydroxy, oxo, or carboxamido group at the 4 position have been reported as highperformance antiwear and antioxidant additives [41], it was the first trial to use molecules with TEMPO attached to an alkyl chain via an amide linkage as an OFM. We suppose that the free radical and amide group provide strong surface adsorption and the rigid ring helps to carry normal loads. Pin-on-disk type tribological tests demonstrated that C 12 Amide-TEMPO exhibited higher load-carrying capacity and more stable sliding than stearic acid [25].
In this study, besides friction properties, the antiwear performance of C 12 Amide-TEMPO was measured. GMO was included as a benchmark in addition to stearic acid which is a model OFM highly effective in friction reduction but causing metal corrosion [42]. Moreover, to understand the effect of the head group chemistry, we compared C 12 Amide-TEMPO with C 12 Ester-TEMPO and C 12 Amino-TEMPO, in which ester and amino linkages replace the amide linkage in C 12 Amide-TEMPO, as illustrated in Figs. 1(b) and 1(c). The comparison included experimentally measured friction properties and theoretically calculated molecular reactivity and surface adsorption properties. Based on the experimental and calculation results, we proposed a model of double-layer adsorption for C 12 Amide-TEMPO, which is unique and is probably one reason for the superior tribological performance of C 12 Amide-TEMPO as compared with the other OFMs used in this study.

Lubricants
As described in Section 1, C 12 Amide-TEMPO, C 12 Ester-TEMPO, C 12 Amino-TEMPO, GMO, and stearic acid were used as OFMs in this study. Their chemical structures are illustrated in Fig. 1, and their molecular weights are 353.57, 354.55, 339.58, 356.54, and 284.48 g/mol, respectively. A hexane solution (100 mg/mL) of GMO, (purity: 99%) was obtained from Olbracht Serdary Research Laboratories and used after removing hexane. Stearic acid (purity: > 98.0% (T)) was obtained from Tokyo Chemical Industry and used as received. C 12 Amide-TEMPO and C 12 Amino-TEMPO were synthesized by the reported methods [43,44]. C 12 Ester-TEMPO was synthesized by a slight modification of the reported method as follows [45]. A solution of dodecanoyl chloride (2.1 mL, 8.8 mmol) in tetrahydrofuran (10 mL) was slowly added to a cool (0 °C) solution of 4-hydroxy-TEMPO (1.7 g, 9.9 mmol) and triethylamine (4.2 mL, 30 mmol) in tetrahydrofuran (10 mL) under Ar atmosphere. The reaction mixture was stirred for 21 h at 30 °C. After removing the tetrahydrofuran under the reduced pressure, the residue was dissolved in EtOAc (100 mL) and washed with saturated NaHCO 3 (aq, 100 mL). The aqueous phase was back-extracted with EtOAc (100 mL × 2), and the combined organic phase was dried over Na 2 SO 4 , evaporated, and dried under reduced pressure to give a crude product, which was purified by the normal-phase medium-pressure liquid chromatography (the ratio of hexane:EtOAc is from 97:3 to 76:24) to afford C 12 Ester-TEMPO (2.5 g, 80%): LRMS (EI) calcd for C 21  The base oil used was synthetic oil poly-alphaolefin (PAO) with the viscosity of 30.3 cSt at 40 °C and 5.79 cSt at 100 °C. Each OFM was dissolved in PAO by stirring for approximately 30 min at the temperature of 65 °C. The concentration was determined to be 0.5 wt% based on the friction reduction performance of 0.1, 0.5, 1.0 wt% C 12 Amide-TEMPO solutions (Fig. S1 in the Electronic Supplementary Material (ESM)). All the solutions were clear at the temperature of 40 °C used for tribological tests.
To investigate the effect of the free radical in the TEMPO-type OFMs, we synthesized compounds by replacing the oxygen radical with hydrogen (H-), methyl group (CH 3 -), or acetyl group (CH 3 CO-). We also tried to use commercially available stearamide [CH 3 (CH 2 ) 16 CONH 2 ], which has the alkyl chain and amide group but not the TEMPO group as compared with C 12 Amide-TEMPO. However, these compounds were not used for tribological tests because they are not soluble in PAO at the concentration of 0.5 wt%.

Tribological tests
The pin-on-disk type unidirectional tribotester illustrated in Fig. 2 was used for tribological tests. The sliding pins were balls of 8 mm in diameter, and the disks were square plates of 30 mm in length and width and 1 mm in thickness. Both the pins and disks were made of SUS304 stainless steel. The pins and disks were purchased and used after rinsed with hexane for 5 min. The surface roughness was measured by the atomic force microscope (Dimension Icon, Bruker AXS) using three pins and three disks. The measurement area was 20.0 μm × 20.0 μm. The average values of the arithmetic mean roughness (R a ) and root-mean-square roughness (R q ) were 15.1 and 21.4 nm for the pins, and 0.76 and 1.33 nm for the disks [25].
In this study, 2 mL lubricants were filled in the container of the tribotester, flooding the gap between the pin and disk. The temperature of the lubricants was kept constant at 40 °C with a heater embedded under the oil container. The sliding radius and rotational speed (r and ω in Fig. 2) were fixed at 6.5 mm and 30 r/min, respectively, giving rise to a sliding velocity of 20.4 mm/s. Two types of tribological tests were performed. One type was to assess the load-carrying capacity of the OFMs by increasing the normal load from 1.0 to the limit of 43.7 N of the tribotester (i.e., mean Hertzian contact pressure of 0.35-1.23 GPa). At each normal load, sliding was performed for 5 min, and the frictional forces measured in the last 3 min were averaged as the final result.
The tests with the increased normal loads were continuously conducted at the same sliding track. The other type was to assess the stability of friction and antiwear performance of the OFMs with sliding at a fixed normal load for 1 h. During sliding, the change of frictional force was measured with time, and after sliding, the wear of the pin and disk was measured with a laser microscope (LEXT OLS5000, Olympus). The normal load was set to be 5.0, 29.2, or 43.7 N (i.e., mean Hertzian contact pressure of 0.60, 1.08, or 1.23 GPa), and the new pin and disk were used for each normal load. The minimum film thickness h min and the dimensionless lambda ratio Λ were calculated using Eqs. (1) and (2), respectively [46,47].
where R is the radius of the sliding pin, 0  is the lubricant viscosity at the atmospheric pressure, u is the mean sliding velocity of the pin and disk, E is the reduced Young's modulus,  is the pressureviscosity coefficient, F is the normal load, k is a contact ellipticity parameter (equal to 1 in this study), and R qp and R qd are the root-mean-square roughnesses of the pin and disk, respectively. With the normal loads 320  [25], min h and Λ were calculated to be no larger than 3.94 nm and 0.18, respectively, showing that all the tests were conducted in the boundary lubrication regime.

Quantum mechanical calculations
To gain insight into the influence of the molecular structure of TEMPO-type OFMs, we carried out two types of Quantum mechanical (QM) calculations using density functional theory (DFT). First, molecular geometries were optimized, and electrostatic potentials (ESPs) were calculated using the Gaussian 16 package [48], in order to understand the molecular reactivity. The M06-2X hybrid functional [49] was used in conjunction with the 6-31G(d) basis set [50][51][52]. Frequency calculations at the same level were performed to ensure that the optimized results corresponded to energy minima.
Then, DFT calculations of TEMPO-type OFMs on iron oxide surfaces were carried out using the Vienna ab initio Simulation Package (VASP) with the projector augmented wave (PAW) method, in order to identify the most stable adsorbed structures and quantify the adsorption energies. Following Ref. [53], α-Fe 2 O 3 (0001) was used as the iron oxide surfaces and modeled as a single Fe-terminated 6-layer slab 10.07 Å × 15.105 Å (i.e., 2 × 3 hexagonal supercell) in length and width. Each Fe bilayer is ferromagnetic, and adjacent bilayers are coupled antiferromagnetically [53,54]. Electronic correlations in the Fe 3d orbitals were accounted for by adding a Hubbard 4eV U J   (in the Dudarev approach [53,55]). This results in an indirect band gap of 1.71 eV, which is within the experimentally observed range (1.38-2.09 eV [56]). Because the adsorption of OFMs on the solid surfaces is mostly determined by the strong Coulomb interaction of the functional groups rather than the weak van der Waals interaction of the alkyl chain, C 3 Amide-TEMPO, C 3 Ester-TEMPO, and C 3 Amino-TEMPO were used to reduce the calculation time. The surface coverage of these OFM molecules was 0.75 molecule/nm 2 , sufficiently low to avoid intermolecular interactions. The iron oxide surface and OFM molecules were first geometrically optimized separately, and then the complexes of each of the OFM molecules on the iron oxide surface were geometrically optimized. Periodic boundary conditions were applied to the in-plane directions, while a vacuum layer at least 15 Å thick was set in the out-of-plane direction to prevent interactions between the neighboring cells. The adsorption energy ad E was calculated as where sys E , sub E , and mol E are the total energies of the optimized complex, solid substrate, and OFM molecule, respectively. Also following Ref. [57], the optB86b-vdW functional was used to include van der Waals interactions, and all calculations were spin-polarized. The plane-wave cutoff was set to 550 eV, and a Monkhorst-Pack k-point mesh of 4 × 4 × 2 was used. A dipole correction was also applied.

Load-carrying capacity and stability of friction
First, the load-carrying capacity of C 12 Amide-TEMPO, GMO, and stearic acid was compared from the change in the friction coefficient with increasing normal load (Fig. 3). The friction coefficient of C 12 Amide-TEMPO www.Springer.com/journal/40544 | Friction remains at a low level even under high loads, whereas the friction coefficients of GMO and stearic acid increase obviously with load. The three OFMs are roughly equally effective in friction reduction under loads less than 5 N; however, beyond that load, C 12 Amide-TEMPO is evidently more effective than GMO and stearic acid. The friction coefficient of GMO is comparable to that of stearic acid under loads less than 20 N, whereas beyond that load, the former is lower than the latter. These results demonstrate that the load-carrying capacity ranks in the order: C 12 Amide-TEMPO >> GMO > stearic acid. Although the load-carrying capacity of C 12 Amide-TEMPO is yet to be determined due to the constraint of the upper load of the tribotester, we can conclude from Fig. 3 that it is larger than 1.2 GPa in terms of mean Hertzian contact pressure or 1.8 GPa in terms of maximum Hertzian contact pressure. Then, the stability of friction was compared for C 12 Amide-TEMPO, GMO, and stearic acid from the time evolution of the friction coefficient during 1-h sliding tests (Fig. 4). The normal load was 5.0, 29.2, and 43.7 N (i.e., mean Hertzian contact pressure of 0.6, 1.1, and 1.2 GPa) for C 12 Amide-TEMPO, but the highest load of 43.7 N was not applied to GMO and stearic acid because they are ineffective at this load as confirmed from Fig. 3. Table 1 shows the time-averaged friction coefficient of the 1-h sliding tests. Aside from the time-averaged values, it is noteworthy from Fig. 4 that in contrast to the large fluctuation in the friction coefficient observed for GMO and stearic acid, C 12 Amide-TEMPO exhibits stable low friction during the 1-h sliding tests. The fluctuation of the friction coefficient of GMO is comparable to that of stearic acid at the relatively low load of 5.0 N, whereas it is smaller than that of stearic acid when the load increases to 29.2 N. These results demonstrate that the stability of friction ranks in the order: C 12 Amide-TEMPO >> GMO > stearic acid, which is consistent with the rank of load-carrying capacity. Note that the friction coefficient of C 12 Amide-TEMPO was relatively large and unstable initially, and it decreased to a stable low value with time. When the disks were treated with oxygen plasma for 1 min, the friction coefficient in the initial period decreased to some extent, whereas the steady-state friction coefficient remained roughly unchanged (Fig. S2 in the ESM). These results are consistent with Ref. [58], indicating that surface cleaning procedures largely affect the friction coefficients at the initial state rather than at the steady state. Therefore, for easy sample preparation, all the disks and pins were not treated with oxygen plasma and were only rinsed with hexane for 5 min in this study.

Antiwear performance
Finally, the antiwear performance of C 12 Amide-TEMPO, GMO, and stearic acid was compared. From the topography of the wear scar on the disk and pin after the 1-h sliding tests, wear was observed for all the disks (Fig. 5), whereas accumulation was more frequently observed than wear for the pins (Fig. S3 in  the ESM). Therefore, as will be described below, we analyzed only the data for wear of disk to quantitively assess the antiwear performance. For direct visual comparison, the cross-sectional profiles along the horizontal dashed lines in Fig. 5 are shown in Fig. 6. It is evident that among the three OFMs, C 12 Amide-TEMPO exhibits the best antiwear performance, giving rise to the narrowest, shallowest, and smoothest wear tracks. This is consistent with the literature showing that the addition of TEMPO and TEMPO derivatives can largely improve the antiwear performance of lubricating oils [41]. Figure 7 quantitatively compares the wear track width, specific wear rate, and area-based surface roughness (Sa) of the three OFMs. For reference, the wear volumes on the sliding pins are shown in Fig. S4 in the ESM. Here the specific wear rate was calculated with 3 Wear volume (μm ) Specific wear rate Normal load (N) Sliding distance (mm)  

(4)
The wear track widths and surface roughnesses of the three OFMs and the specific wear rates of C 12 Amide-TEMPO and stearic acid increase with the increasing normal load, whereas the specific wear rate of GMO decreases slightly with the increasing normal load. Compared with GMO and stearic acid, C 12 Amide-TEMPO reduces the wear track width by 37% and 27%, the specific wear rate by 70% and 63%,  the surface roughness by 62% and 70% at the normal load of 5.0 N. At the normal load of 29.2 N, the reduction rates by C 12 Amide-TEMPO as compared with GMO and stearic acid are 24% and 30% for the wear track, 39% and 65% for the specific wear rate, and 32% and 49% for the surface roughness. The wear track width, specific wear rate, and surface roughness for C 12 Amide-TEMPO at the normal load of 43.7 N are even 5%, 30%, and 3% less than those for GMO at the normal load of 29.2 N and 13%, 59%, and 26% less than those for stearic acid at the normal load of 29.2 N. From Table 1, we know that compared with GMO and stearic acid, C 12 Amide-TEMPO reduces the friction coefficient by both 21% at the normal load of 5.0 N and by 20% and 29% at the normal load of 29.2 N. The reduction rate of the specific wear rate and surface roughness by C 12 Amide-TEMPO is 1.6-3.4 times larger than those of the friction coefficients at the normal loads of 5.0 and 29.2 N. Hence, we suggest that the excellent antiwear performance of C 12 Amide-TEMPO may be associated not only with the small time-averaged friction coefficient but also with the small fluctuation over time (i.e., the high stability of friction).

Friction and wear reduction performance
The friction-reduction performances of C 12 Amide-TEMPO, C 12 Ester-TEMPO, C 12 Amino-TEMPO were compared in term of the time evolution of the friction coefficient during 1-h sliding tests (Fig. 8). In contrast to the low and stable friction of the former, the latter two show high and fluctuating friction even though the normal load was as small as 5.0 N. The topography of wear scars and the cross-sectional profiles of the  The friction and wear reduction performance of C 12 Ester-TEMPO and C 12 Amino-TEMPO is even poor as compared with GMO and stearic acid ( Fig. 4(a), Table 1, and Figs. 7(a) and 7(b)). These results demonstrate that the amide group in C 12 Amide-TEMPO is crucial for the observed good tribological performance. The underlying mechanism for the contribution of the amide group and the reason for the poor friction-reduction performance of C 12 Ester-TEMPO and C 12 Amino-TEMPO will be discussed in Section 4. Figure 9 illustrates the molecular ESPs on the 0.001 a.u. electron density isosurface of geometrically optimized C 12 Amide-TEMPO, C 12 Ester-TEMPO, and C 12 Amino-TEMPO. The positions and values of minima and maxima of the ESP were analyzed using the Multiwfn program [59,60] and indicted in Fig. 9. A common feature of the three TEMPO-type molecules is that a large area of strongly negative ESP and two  Figure 10 shows the most stable adsorbed structure of C 3 Amide-TEMPO, C 3 Ester-TEMPO, and C 3 Amino-TEMPO on the Fe 2 O 3 (001) surface. All these molecules lie flat on the surface, thereby maximizing both the number of bonds between the head group and surface and the van der Waals interactions between the alkyl chain and surface. Consistent with the above-described results of molecular ESP, two bonds are developed between the head group and surface: O•-Fe surf and O amide -Fe surf for C 3 Amide-TEMPO, O•-Fe surf and O ester -Fe surf for C 3 Ester-TEMPO, and O•-Fe surf and N amino -Fe surf for C 3 Amino-TEMPO. As noted in Fig. 10, the lengths of these bonds are 1.97-2.13 Å, comparable to the O-Fe bond length (1.94 and 2.09 Å) in bulk hematite [62]. This indicates that the three TEMPO-type OFMs can chemically adsorb on iron oxide surfaces. For C 3 Amide-TEMPO, the lengths of O•-Fe surf and O amide -Fe surf are equal, suggesting that the oxygen radical and amide oxygen contribute equally to the chemisorption. In contrast, the length of O•-Fe surf is slightly shorter than those of the other bonds for C 3 Ester-TEMPO and C 3 Amino-TEMPO, suggesting that the oxygen radical is more responsible for the chemisorption than the ester and amino groups. The adsorption energies for these most stable structures are shown in Table 2. For comparison, the adsorption energies of hexanoic acid  | https://mc03.manuscriptcentral.com/friction (HA:CH 3 (CH 2 ) 4 COOH) and glyceryl monohexanate (GMH:CH 3 (CH 2 ) 4 COOCH 2 CHOHCH 2 OH) from Ref. [53], which have the same head group as stearic acid and GMO but a shorter alkyl chain, are also presented in Table 2. It should be noted that the negative sign of the adsorption energies indicates attractive interactions, and the absolute value indicates the adsorption strength. C 3 Amide-TEMPO shows the strongest adsorption, approximately 1.7 and 1.3 times stronger than those of HA and GMH. It should be noted that besides the structure shown in Fig. 10(a), C 3 Amide-TEMPO can also adsorb on the iron oxide surfaces via O•-Fe surf and H amide -O surf with an adsorption energy of −69.6 kcal/mol (Fig. S7 in the ESM). C 3 Ester-TEMPO and C 3 Amino-TEMPO also exhibit stronger adsorption energies than those of HA and GMH, which however cannot explain their poor friction-reduction effect as compared with stearic acid and GMO. Consequently, we infer that strong surface adsorption is a necessary but not a sufficient condition for good tribological performance of OFMs. Further detailed discussion will be given in Section 4. Glyceryl monohexanate −73.6

Discussion
As described in Section 3.1, C 12 Amide-TEMPO outperforms GMO and stearic acid, particularly for load-carrying capacity, stability of friction over time, and antiwear performance. These experimental results suggest that the C 12 Amide-TEMPO boundary films are more durable against heavy-loaded and prolonged sliding than the boundary films of GMO and stearic acid. As described in Section 3.2.1, the friction and wear reduction effect of C 12 Amide-TEMPO is greatly superior to those of C 12 Ester-TEMPO and C 12 Amino-TEMPO. Therefore, we suggest that the two functional groups in C 12 Amide-TEMPO, i.e., the amide and free oxygen radical, are crucial for ensuring the durability of the boundary films. The conceivable reasons are elaborated below.
As illustrated in Fig. 11, we consider that the contribution of the amide group and oxygen radical is three folds. First, the amide oxygen and free radical interact chemically with iron oxide surfaces, thereby forming a strong surface adsorption layer. As suggested by the results in Table 2, C 12 Amide-TEMPO shows higher adsorption energy on iron oxide surfaces than C 12 Amino-TEMPO, C 12 Ester-TEMPO, and the conventional OFMs of GMO and stearic acid. Second, because the amide serves as both hydrogen bond donor and acceptor and the oxygen radical serves as the hydrogen bond acceptor, they help to form a diffusive layer on the adsorbed one as in electric double layers through the interlayer hydrogen-bonding of H amide -O• or H amide -O amide . Note that the interaction energies of the two types of hydrogen-bonding were calculated with VASP to be −11.6 and −10.8 kcal/mol. Third, intralayer hydrogen-bonding can also form in each of the two layers between H amide -O• or H amide -O amide . Such double-layer structure induced by both surface interactions and interlayer and intralayer hydrogen-bonding interactions has not been reported in the literature to our knowledge, and it is difficult to be formed by C 12 Ester-TEMPO, C 12 Amino-TEMPO, and the conventional OFMs of GMO and stearic acid, as will be described later. We suggest that in addition to strong surface adsorption, the interlayer and intralayer hydrogen-bonding also increases the strength of the boundary films by enhancing the cohesion strength, thereby rendering the films difficult to be sheared off during heavily-loaded and long-time www.Springer.com/journal/40544 | Friction sliding. Moreover, the upper layer might serve as a buffer to protect the surface adsorption layer, which is the last barrier to prevent solid-solid contacts, against shear. Therefore, we suggest that the good tribological performance of C 12 Amide-TEMPO, particularly the high load-carrying capacity, high stability of friction, and excellent antiwear performance as compared with GMO and stearic acid, is likely attributed to the unique double-layer structure of the boundary films.
As seen from Fig. 1, stearic acid has only one functional group. GMO has two functional groups; however, it is more energetically stable with both of its functional groups adsorbed on iron oxide surfaces, as indicated by the QM calculations [53]. Consequently, once stearic acid and GMO adsorb on solid surfaces, they are difficult to interact with other molecules, and thereby difficult to form the double-layer structure like C 12 Amide-TEMPO (Fig. 11). C 12 Ester-TEMPO and C 12 Amino-TEMPO are also difficult to form the boundary films with the double-layer structure for the reasons described below. As seen from Fig. 9, C 12 Ester-TEMPO is difficult to develop intermolecular interaction, whereas the hydrogen-bonding of H amino -O• can be developed between C 12 Amino-TEMPO molecules. However, when C 12 Amino-TEMPO molecules adsorb on the surfaces via O• and N amino , they are difficult to interact with other C 12 Amino-TEMPO molecules via H amino -O•. The reason is as follows. As seen from Fig. 10(c), the bond angle of H amino -N amino -Fe surf is 88.4°. It is much smaller than the bond angle of 109.5° in nitrogen-centered tetrahedral structure, demonstrating that an agnostic-like interaction exists between H amino and Fe surf . Due to this interaction, H amino is pulled close to the iron oxide surface, with its distance from Fe surf being 2.37 Å, and its bond length with N amino being slightly elongated to 1.03 Å as compared with 1.02 Å in the isolated C 3 Amino-TEMPO. As a result, H amino is difficult to be approached by O• of other C 12 Amino-TEMPO molecules, and an upper layer on the surface-adsorbed molecules is difficult to form.
However, the above-described difference is not sufficient to explain the far inferior tribological performance of C 12 Ester-TEMPO and C 12 Amino-TEMPO even as compared with GMO and stearic acid. The poor performance even at the low normal load of 5.0 N suggests that C 12 Ester-TEMPO and C 12 Amino-TEMPO are difficult to form effective boundary films. Formation of effective boundary films involves two processes for OFMs: first approaching solid surfaces, and then interacting with surface active sites. As C 12 Ester-TEMPO and C 12 Amino-TEMPO show larger adsorption energies than GMO and stearic acid (Table 2), we suggest that C 12 Ester-TEMPO and C 12 Amino-TEMPO are difficult to approach solid surfaces. The reason probably lies on the low polarity of C 12 Ester-TEMPO and C 12 Amino-TEMPO, which renders them highly soluble in the nonpolar base oil of PAO and thus difficult to diffuse and approach to solid surfaces. Previous studies have also demonstrated that OFMs with high solubility in oils are generally less effective [64].

Conclusions
To establish a new class of OFMs, we assessed the friction and wear reduction performance of our synthesized C 12 Amide-TEMPO, which is characterized by a TEMPO-based head group consisting of an amide linkage, a rigid six-membered ring, and a free oxygen radical terminal. In contrast to the conventional OFMs of GMO and stearic acid, whose friction coefficients increase with the normal load, the friction coefficient of C 12 Amide-TEMPO remains at a low level even at the limit load of 43.7 N of the tribotester. Even compared with GMO and stearic acid at their effective load of 5.0 N, C 12 Amide-TEMPO exhibits considerably more stable instantaneous friction coefficient and reduces the specific wear rate and surface roughness of wear tracks by more than 60%.
Moreover, we investigated the effect of the amide group by comparing C 12 Amide-TEMPO with C 12 Ester-TEMPO and C 12 Amino-TEMPO for friction properties measured experimentally and molecular reactivity and surface adsorption properties calculated with the QM methods. The friction reduction effect of C 12 Amide-TEMPO is far superior to those of C 12 Ester-TEMPO and C 12 Amino-TEMPO, highlighting the critical role of the amide group. We suggest from the QM calculation results that the boundary films formed by C 12 Amide-TEMPO have a unique double-layer | https://mc03.manuscriptcentral.com/friction structure. A strong surface adsorption layer is developed by the chemical interactions of the amide oxygen and free radical with iron oxide surfaces, and an upper layer is formed by the interlayer hydrogen-bonding between the amide hydrogen and free radical or the amide hydrogen and oxygen. Besides, the two types of hydrogen-bonding can form in each of the two layers. We suggest that the strong adsorption and interlayer and intralayer hydrogen-bonding enhance the strength of the boundary films to withstand long-time and heavily-loaded sliding, thereby leading to the high tribological performance of C 12 Amide-TEMPO. The findings in this study are expected to provide new hints for future research on the molecular design of OFMs.