From ultra-low friction to superlubricity state of black phosphorus: Enabled by the critical oxidation and load

Based on the density functional theory (DFT), we investigate the friction properties of inevitable oxidized black phosphorus (o-BP). o-BP with the weaker interlayer adhesion exhibits their great potential as a solid lubricant. At the zero load, the friction property of o-BP is adjusted by its oxidation degree. Expressly, ultra-low friction of P4O2 (50% oxidation, O : P = 2 : 4 = 50%) is obtained, which is attributed to the upper O atoms with lower sliding resistance in the O channel formed by lower layer O atoms. More attractive, we observe superlubricity behavior of o-BP at the critical load/distance due to the flattening potential energy surface (PES). The flattening PES is controlled by the electrostatic role for the high-load (P4O3, O : P = 3 : 4 = 75%), and by the electrostatic and dispersion roles for the low-load (P4O2). Distinctly, the transform from ultra-low friction to superlubricity state of black phosphorus (BP) can be achieved by critical oxidation and load, which shows an important significance in engineering application. In addition, negative friction behavior of o-BP is a general phenomenon (Z > Zmin, Zmin is the interlayer distances between the outermost P atoms of minimum load.), while its surface-surface model is different from the fold mechanism of the tip-surface model (Z0 < Z < Zmin, Z0 is the interlayer distances between the outermost P atoms of equilibrium state.). Thus, this phenomenon cannot be captured due to the jump effect with instability of the atomic force microscopy (AFM) (Z > Zmin). In summary, o-BP improves the friction performance and reduces the application limitation, comparing to graphene (Gr), MoS2, and their oxides.


Introduction
Friction and wear are major contributors of energy loss and failure in all types of mechanical systems, such as engines [1]. According to the Ref. [2], friction consumes a third of the world's primary energy. Therefore, effectively controlling and reducing the friction and wear of moving machinery can improve the efficiency and life of mechanical parts. Lubrication is one of the main purposes to reduce friction and wear of moving machinery and may be liquid or solid [3].
At present, it has been reported that the contact pressures in the liquid lubrication systems are up to ~7.5 MPa (polymer brushes) [4], ~10 MPa (water-lubricated self-mated ceramics) [5], and ~300 MPa (polyhydroxy alcohol/acid mixtures) [6,7]. Although the contact pressures in liquid lubrication systems can be satisfied for some applications (e.g., manmade joints), the use of solid lubricants is strictly required to instead liquid lubrication in some operating conditions [8]. The most common example involves the applications of aerospace/space, in which the liquid lubricant is unusable under low temperatures because they become too sticky to lubricate effectively and may even solidify [9,10]. Among solid lubricants currently, graphene (Gr) [11] and molybdenum disulfide (MoS 2 ) [12] hold special important place. As a sheet solid material, it consists of single atom-thin planes that can easily slide over each other. Moreover, the lubricative properties were improved drastically under specially conditions, such as wet condition of Gr [13] and anoxic condition of MoS 2 [14]. However, oxidation is always inevitable whatever atmosphere (i.e., oxygen) or space (i.e., atomic oxygen) environments. It is reported that friction of Gr [15,16] and MoS 2 [17] by oxidation were drastically enhanced. Obviously, the limitations of Gr and MoS 2 could not well satisfy some of the aerospace/space application environments (such as high vacuum and high-energy atomic oxygen). Thus, the attempts to obtain stable lubricity under a harsh condition of industrial applications are required eagerly.
Among all the attractive two-dimensional (2D) materials, the single-or few-layer black phosphorus (BP) had been rediscovered [18], and became the focus of study in the 2D semiconductor fields due to its direct band gap and high carrier mobility [19]. In addition, similar to the structures of Gr and transition-metal dichalcogenides (TMDs), BP is also made of weak van der Waals (vdW) interactions between layers. Therefore, BP layers are more easily sheared between each other, which presents the larger potential of friction applications. Phosphorene with the commensurate or incommensurate structures showed the excellent friction performance, based on molecular dynamics (MD) simulations [20]. Specially, the superlubricity from the armchair-zigzag orientation was shown by density functional theory (DFT), which is responsible for the flat potential energy surface (PES) [21]. Similarly, one of the biggest challenges for applications of BP is mainly focused on its stability [22,23], which is prone to oxidizing when exposure to water, oxygen, and visible light [24]. However, different from Gr, MoS 2 , and their oxides, a partially oxidized black phosphorus (o-BP) with robust liquid superlubricity can be achieved [25,26], which was attributed to that water molecules could be retained at the friction interface owing to the abundant P=O and P-OH bonds of the o-BP surface. A friction reduction of about 50% at the degraded area of the BP was observed using the atomic force microscopy (AFM), which was attributed to the formed phosphorus oxides [27]. The interfacial shear stress (ISS) as low as 0.029 ± 0.004 MPa of the degraded BP/SiO 2 interface was observed by the AFM, being comparable to that of incommensurate rigid crystalline contacts [28]. This super-slippery resulted from significantly water layers attached to the POH and SiOH groups due to ambient degradation, which greatly weakened their direct interaction and separated their contact area. Distinctly, the friction performance of o-BP as a solid lubricant may be more prominent than those of Gr and MoS 2 , as well as of Gr and MoS 2 oxides.
In the field of microscopic friction, although the investigation of friction performance between o-BP and different friction pairs (tip/o-BP or o-BP/substrate) was increased significantly using the AFM, the study of its self-lubrication performance (o-BP/o-BP) has not been paid more attention to. It is not clear whether o-BP as solid self-lubrication has a better friction property. But, o-BP with reduced friction may be very hopeful referring to the reports above [25][26][27][28]. To the best of our knowledge, the studies of friction behavior and mechanism of o-BP/o-BP have not been studied extensively, which are worth looking forward to friction property. On the one hand, the microscopic friction mechanism of o-BP/o-BP can also reveal the macroscopic friction of o-BP that is solid self-lubrication. On the other hand, the research for the self-lubrication performance of o-BP/o-BP provides a certain reference for seeking new materials to adapt to the harsh environment of the aerospace/space mechanical lubrication field, due to enhanced friction of Gr and MoS 2 by oxidation.
In this work, the binding energy of o-BP is studied firstly to obtain its stable structure in Part 2 in the Electronic Supplementary Material (ESM). What is more, the barrier potential and friction of o-BP are calculated to identify the effect of oxidation degree to its friction performance under different loads. Finally, the differential charge density and density of states (DOSs) are shown to analyze the mechanism of o-BP with excellent friction performance.

Calculation methods
The DFT is carried out through the Cambridge Sequential Total Energy Package (version 21.1.1, CASTEP, Cambridge Enterprise Limited, UK) [29,30] to describe the friction mechanism of o-BP. Calculations are performed using the generalized gradient approximation (GGA) and the PerdewBurkeErnzerhof (PBE) functions [31]. The vdW interaction with the Grimme (DFT-D2) function is induced to capture the interactions between the layers [32]. A kinetic energy cutoff is set to be 500 eV, and the Brillouin zone integration using the Monkhorst-Pack scheme is sampled with 11 × 11 × 1 for cell optimization [33]. The z dimension of vacuum is enlarged to 15 Å at least to avoid the possible effects between replicated images. During relaxation, the value of HellmanFeynman force is allowed as low as 0.02 eV/Å for every steps. The convergence of energy is chosen to be 2×10 −6 eV [33]. Based on the parameters above, the structures of o-BP are optimized and analyzed to explain its physicochemical properties.
In the friction simulation using DFT, two methods (the equal load and interlayer distance) are usually used. The latter is carried out in our work, and their advantages and disadvantages have been described in Ref. [34]. The effect of load is modeled by fixing the z coordinate of o-BP (the outermost P atoms) to form bilayers with the different interlayer distances Z (Fig. 1). The interlayer load is evaluated as the opposite of the residual force F n on the fixed atoms. Based on the experience about the atomic scale friction [35] of Zhong and Tománek [36], the loads F n are approximated by the interlayer distance Z and binding energy E b (i.e., F n = −∂E b /∂z) [37]. The static lateral forces f static is determined by calculating the energy dissipation of the minimum energy path (MEP) (i.e., f static = ∆E/∆x, where ∆E is the energy barrier of Min and Saddle (Min represents the equilibrium position of MEP, and Saddle represents the largest energy position of MEP), and ∆x represents the sliding distance).

Structures and properties of o-BP
It is well-known that the newly stripped BP can be oxidized firstly under the atmospheric environment (i.e., O 2 , H 2 O, and ultraviolet light) in just a few hours [24,38]. In Ref. [39], the oxidation and decomposition of BP have been quite controversial, which result from the dominated role of water and oxygen molecules [38,40]. The three-step degradation processes of BP (the generation of superoxide under light, the dissociation of the superoxide, and the eventual breakdown under the action of water) were proposed by Zhou et al. [24] based on DFT and MD calculations, which had temporarily ended the controversy above. Remarkably, the high-oxidized BP (i.e., POP bonds) is the native umbrella to prevent the attack of water molecules. Thus, the models associated with water molecules (i.e., OHBP and HBP) are excluded out  as OH and H groups, respectively, which would shear the BP to fragments [41]. Based on the reports above, the structures of o-BP with different oxidation degrees are established to study its friction properties.
Calculation of the atomic scale showed that the bilayer structure may be the key to determining the friction properties of 2D material [34,42]. Ten models of o-BP with a bilayer structure are built, and are all in thermodynamically stable (the binding energy: −1,457.632−1,181.211 meV/(8·atom)) in Fig. S1 and Tables S1 in the ESM. Here, to save on the computational resources, four modes are selected as representees of o-BP, namely P8 (O : P = 0 : 8 = 0%), P8O (O : P = 1 : 8 = 12.5%) [38,43], P4O2 (O : P = 2 : 4 = 50%) [44], and P4O3 (O : P = 3 : 4 = 75%) [24] in Fig. 1. Moreover, the system of P4O (O : P = 1 : 4 = 25%) is also considered in Fig. S9(a) in Part 2 of the ESM in order to maintain the integrity of the calculation system. However, we believe that the particularity of P4O structure has been included in Figs. 1(b) and 1(d), regardless of O atom positions or interface structures of o-BP. Thus, there is no more discussions of P4O in the main text, and more details are described in Part 2 (Figs. S9, S10, S11, and S12, and Tables S2 and S3) of the ESM. Compared to those of P8, the remaining structures show varying degree folds, and the cell volumes (a and b) gradually increase ( Fig. 1 and Table 1). Those changes stem from that O atoms enter the BP lattice, which causes the strange chemical bond (P=O/POP) and lattice expand [43]. DOSs of o-BP also further identify the interaction of O and P atoms in Fig. 2. The number of 2s orbital peaks (0, 1, Table 1 Geometry parameters of o-BP, such as the lattice constant (a and b (Å)), the intralayer distance (d (Å)) between the innermost P or O atoms, the bond length (R 1 , R 2 , and R 3 (Å)), and the bond angle (θ 1 and θ 2 (°)).   [45], in which the number of peaks corresponds to the oxidation degree of BP. In particular, the peak position of the intralayer O in P4O3 is about 3 eV lower than those of others, which may be used to determine the oxidation kind of BP in the experiments. As the increased oxidation, the Fermi energy level of DOSs for P8 and P4O3 are steeper than those for P8O and P4O2, which may affect the electron transport characteristics and surface activity of BP [45]. These phenomena above indicate that the geometrical and physicochemical properties of BP are severely altered by oxidation. More importantly, as the oxidation increases, the intralayer distance d decreases from 3.492 to 1.504 Å. On the one hand, this may stem from the positively charged P and negatively charged O atoms between o-BP layers, which causes an electrostatic attraction in Fig. 1. On the other hand, the electrons of P atoms are highly localized around O atoms due to the poor electronegativity of P than O atoms, which reduces the interfacial repulsion. Moreover, the increased binding energies (−1,352.680(−1,181.580) meV/(8·atom)) and reduced DOS localizations (−100 eV) of o-BP are also obtained as the increased oxidation in Table 2 and Fig. 2, respectively. These mean lower interfacial interactions and weaker slip resistance [46], and thus oxidation of BP may induce better lubrication properties.

Ultra-low friction behavior of BP induced by oxidation at zero load
The atomic-scale friction of 2D materials have been explained by particle behavior, suggesting that the particle movement always follows MEP even in the existed external loads and special orientations [47].
To determine the MEP of o-BP, the PESs at zero load are plotted in Fig. 3. The blue region represents the Min energy regions (i.e., the position of the right geometric image). The system produces red high energy regions when the upper and lower layers of o-BP move relatively. As shown in Figs. 3(a) and 3(b), P8 and P8O have similar PES structures, which mainly stem from that the electronic structure of interface in P8O, is not altered barely when the outside surface of BP is oxidated. Although the PES strength of P8O is reduced by the outside surface oxidation, the anisotropy is still clear due to the performance differences of the "armchair" and "zigzag" directions [48]. When P8 is oxidized to P8O, the sliding barrier of path 2 (ABAAAB) is reduced from 111.580 to 99.560 meV/(8·atom), and the one of path 3 (ABACAB) is reduced from 167.210 to 127.290 meV/(8·atom) (Figs. S2(a) and S2(b) in the ESM). The role of oxidation is also further confirmed by the increased binding energy from P8 (E bl : −1,352.680 meV/8·atom, E bh : −1,186.610 meV/(8·atom)) to P8O (E bl : −1,263.380 meV/(8·atom), E bh : −1,135.890 meV/(8·atom)) in Table  2. The reduction of the maximum sliding barrier and increased binding energy cannot effectively indicate the reduction of interfacial friction, but it implies that the outside surface oxidation is contribute to the peeling of BP. Importantly, P4O2 and P4O3 are formed based on the separating BP from P8O. For P4O2 and P4O3, the sliding barriers of path 2 (ACA) are 204.770 and 253.690 meV/(8·atom), while the ones of path 3 (ADA) are 175.150 and 190.160 meV/(8·atom) in Figs. S2(c) and S2(d) in the ESM, respectively. The maximum sliding barriers of P4O2 and P4O3 are higher than those of P8 and P8O, which corresponds to a larger static lateral force (f static )in Figs. S2(e) and S2(f) in the ESM, respectively. This may be derived from that the structural wrinkles and electronic localization of the former are more enhanced due to the more Table 2 Sliding barriers (ΔE = E max − E min , (meV/(8·atom))), static lateral forces (|f static |, (meV/(Å·8·atom))), average lateral forces (|f average |, (meV/(Å·8·atom))), low (E bl , (meV/(8·atom))) and high (E bh , (meV/(8·atom))) binding energies of o-BP.   Table 2. This contradictory phenomenon further suggests that the sliding friction path is selective rather than arbitrary. With the oxidation of BP, although the maximum sliding barrier of the interface is enhanced, MEP is formed gradually in Figs Table 2. The sliding barrier of P4O2 is about 2/3 times lower than that of P8, which produces excellent lubricating property than others. Especially, the barrier of P4O2 (ΔE: 21.160 meV/(8·atom)) is lower than that of Gr (ΔE: 58.120 meV/(8·atom)) and MoS 2 (ΔE: 67.824 meV/(8·atom)) [34], as well as o-Gr (ΔE: 33.520 meV/(8·atom)) [15] and o-MoS 2 (ΔE: 720.000 meV/(8·atom)) [17], which suggests that ultra-low friction of o-BP is better than those of Gr, MoS 2 , and their oxides. It is noted that the interfacial sliding barrier of P4O is 57.900 meV/(8·atom), locating one between P8 and P8O in Fig. S10(c) and Table S3 in the ESM. This suggests that the relationship of oxidation degree and tribological property may not change linearly. On the one hand, these imply that the oxidation of BP is beneficial for the reducing friction. On the other hand, the friction property of o-BP is mainly determined and to be adjustable by its oxidation degree. The speculations above are further confirmed by the |f static | and |f average | of o-BP in Fig. 5(b), Table 2, and Fig. S10(d) and Table S3 in the ESM.
To study the friction mechanism induced by the interlayer interactions of o-BP, Bader charge analysis [50] is presented with the charge transfer between P=O bonds. The charges are transferred from P to O atoms, resulting in positively charged P and negatively charged O atoms in Figs. 1(b)1(d). Thus, the interlayer of o-BP shows as the attraction force when     Figs. 3(b) and 3(c). This low friction mechanism of o-BP is similar to that of the MoS 2 /MoO 3 heterostructure [51].
In summary, the friction performance of o-BP as a solid lubricant is more prominent than those of Gr and MoS 2 , as well as those of Gr and MoS 2 oxides. Moreover, o-BP prolongs the application life of BP, because the full oxidized BP (POP) prevents its surface degradation. On the other hand, the friction properties of o-BP are adjustable by its oxidation degree. These also reflect the potential of BP as an ideal solid lubricating material.

Superlubricity behavior of o-BP induced by the high-load
The binding energies are divided into the two monotonic intervals by the equilibrium position (the dashed positions) in Fig. 6, suggesting that the load and interlayer distance may be not perfectly positively correlated. The minimum binding energies of o-BP (the blue dashed line, Z 0 ) correspond to zero load of the system in Fig. S4 in the ESM. The loads of Z < Z 0 are positively correlative with the interlayer distance. However, the loads of Z > Z 0 are consisting of two monotonic intervals. Therefore, the frictional properties of o-BP under the high-load (Z < Z 0 )/low-load (Z > Z 0 ) should be discussed separately.
In the high-load area, the binding energy intersections of o-BP are found at Z high (P8: 6.126, P8O: 6.366, and P4O3: 8.520 Å) in Fig. 6, in addition to the P4O2. These intersections of o-BP lead to the overlap of the potential energy during the sliding so as showing special friction properties [49]. The sliding barrier of MEP (ABAEAFAEAB or ABA) is concerned mainly to study the effect of the high-load on the friction performance of o-BP. The sliding barrier of AEAF and AB are equal when Z high = 6.126, 6.366, and 8.520 Å in P8, P8O, and P4O3, respectively (Figs. 7(a), 7(b), and 7(d)). As we predict that the friction transition points of P8, P8O, and P4O3 are obtained in Fig. 7(e), 7(f), and 7(h), respectively, except for P4O2. As the load increases, the sliding barrier of P8, P8O, and P4O2 are greater than zero, which implies the positive corrugation and increased friction. The frictions of P8 and P8O drop suddenly at Z high , and then rise slowly, which is mainly due to change of the maximum barriers (from AE to AF), leading to the increased displacement [34]. Compared to that of P4O2, the increased trends of P8 and P8O are more slowly with the increased load, and thus they may present more superiority under the high-load. Moreover, similar tribological trends with P8 and P8O have also been observed for P4O when Z high = 8.119 Å in Figs. S12(c) and S12(d) in the ESM. Interestingly, the sliding barrier of P4O3 are located on both sides of the zero potential energy, and these induce a transformation from corrugation to anti-corrugation of PES [49]. More importantly, the transformation of PES may induce a special superlubricity behavior of P4O3. The friction trend of P4O3 seems to be more attractive, where superlubricity behavior (with zero barrier) is obtained as the load increases (Fig. 7(h)). Moreover, this superlubricity behavior has been found  in Refs. [49,52] such as Gr/Gr, MoS 2 /MoS 2 , Pd/Gr, and Xe/Cu, and is attributed to the critical-transition from anti-corrugating to corrugating systems.
Obviously, superlubricity behavior of P4O3 results from the binding energy cross induced by the interlayer interactions. It is well-known that the interlayer interactions are mainly composed of the electrostatic and dispersion action [53], which imply that superlubricity behavior of P4O3 under the high-load may be dominated through both factors above in Fig. S4 in the ESM. However, that is not the case. The binding energies of A-and B-stacked P4O3 are completely uncorrelated when only dispersion force is considered in Fig. S5(a) in the ESM, implying that the dispersion action is small to the superlubricity behavior of P4O3. However, the intersection of binding energies for A-and B-stacked P4O3 is again obtained when only electrostatic action is considered in Fig. S5(b) in the ESM. Specially, the binding energy intersections of the electrostatic action (Z high-elc ) are exactly coinciding with those of both actions under the high-load, i.e., Z high-elc = Z high = 8.520 Å. Thus, although the electrostatic and dispersive action coexist, the former is the key to determining the superlubricity behavior of P4O3 under the high-loads. Changes of charge density near potential energy cross of Z High (Z = 8.200， 8.520, and 8.900 Å) are shown in Figs. 8(a)8(c), in order to explore the intrinsic mechanism of superlubricity behavior of P4O3 induced by the electrostatic action. The charges of Min and Saddle increase and accumulate near the O atoms, and the latter with a faster polarization rate is gradually close to that of the former at Z high = 8.520 Å in Fig. 8(d). Moreover, DOSs of Min are similar to that of Saddle at Z high = 8.520 Å in Fig. S6 in the ESM. These mean that the energies of Min and Saddle maybe equivalent. Thus, the equivalent interlayer electron states and electron quantities on Min and Saddle may be the key of the potential energy crossover as to inducing the superlubricaty behavior of P4O3.

Negative friction and superlubricity behaviors of o-BP induced by the low-load
The minimum binding energy of (Z > Z 0 ) produces the negative value in Fig. S4 in the ESM, i.e., the attractive force. The electrostatic roles are displayed gradually with the oxidation of BP, where the positively charged P and negatively O atoms are responsible for the attractive force. Thus, the attractive force cannot be ignored on the far PES, suggesting possible negative friction behavior between layers. Although negative friction behavior of BP had not been many observed, this phenomenon has been many reported in other 2D materials [54,55]. Moreover, superlubricity under the low-load likely plays a better role than that under the high-load in the application of nanotechnology, so it is also crucial to focus the friction behavior of the low-load. The low-load regions are divided into two monotonically intervals by Z min (the black dotted line, i.e., P8: 8.000 Å, P8O: 7.800 Å, P4O2: 8.500 Å, and P4O3: 9.600 Å) in Fig. S4 in the ESM. In general, friction is positively correlated with the load, while the Z min extremums further hint the emergence of non-Armandon's area. The sliding barriers (ΔE) and static lateral forces (f static ) of o-BP are reduced as the dwindled load when Z 0 < Z < Z min , while it is also reduced as the magnified load when Z > Z min in Fig. 9, except for especial P4O2. We have predicted that the friction is positively correlated with the load when Z 0 < Z < Z min , while it is negatively correlated with the load when Z > Z min . However, Deng et al. [54] investigated the sliding behavior of diamond tip on the chemically modified Gr surface using the AFM, MD, and finite element analysis, and unexpectedly found that negative friction behavior was also caused by attraction force. The fold mechanism of 2D materials indicated that the increasing friction in negative friction phenomenon is due to the strengthened surface fold and the reducing load during the lifting of the AFM tip. The sliding tip caused a larger fold deformation and contact area of the tipsurface, which thus increased friction [56]. Obviously, the mechanisms above and conclusions are contradictive with negative friction in Z > Z min regions of this work. On the one hand, this contradiction arises mainly from a fact that the formation of surface wrinkle is easier for the tipsurface than the surfacesurface of this work. Negative friction behavior of the tipsurface should be obtained when Z 0 < Z < Z min , which is only attributed to the dispersion force [52]. On the other hand, the electrostatic and dispersion actions appear when Z > Z min (Fig. S4 in the ESM), which is conducive to the stability of the surfacesurface system. More importantly, according to the basic principles of the traditional AFM, the jump effect of instability [57] could be produced when Z > Z min . Therefore, negative friction behavior may be theoretically difficultly captured by the conventional AFM experiments, which may be one of the main reasons why negative friction of surfacesurface currently has not yet been discovered experimentally.
More importantly, the binding energy intersections of P8 and P8O are observed at Z low = 8.178 and 8.050 Å, respectively, but one of P4O3 is instead by P4O2 at Z low = 8.230 Å in Fig. 6. Different from the high-load, the friction jumps of P8 and P8O are not observed clearly at the binding energy intersections in Figs. 9(a), 9(b), 9(e), and 9(f), due to the lower sliding barriers at the far PES. Moreover, similar tribological trends with P8 and P8O have also been observed for P4O when Z low = 9.023 Å in Figs. S12(e) and S12(f) in the ESM. Whereas, the superlubricity behavior of P4O2 is predicted in Figs. 9(c) and 9(g). According to Ref. [58], the interfacial friction behavior of the low-load is mainly determined by the interlayer dispersion force. Although the contribution of the dispersion role is greater than that of the electrostatic role, the latter as the long-range role will not disappear within the range of the dispersion force in Fig. S4 in the ESM. Expressly, the binding energy intersections of the electrostatic (Z low-elc ) and dispersive roles (Z low-D2 ) in P4O2 are observed simultaneously under the low-load, that is, Z low-elc = 8.383 Å and Z low-D2 = 8.100 Å in Fig. S7 in the ESM. These two intersections do not coincide, but Z low = 8.230 Å is just between 8.100 and 8.383 Å. Thus, superlubricity behavior of P4O2 results from the synergistic action of both the dispersion and electrostatic role under the low-load. To further explore the intrinsic mechanism of superlubricity behavior of P4O2 induced by the potential energy intersections under the low-load, the changes of charge density near potential energy cross of Z high (Z = 8.000, 8.230, and 8.600 Å) are calculated in Figs. 10(a), 10(b), and 10(c), respectively. The accumulation of charge between layers is significantly weakened in Figs. 10(a)10(c), suggesting that the interlayer role is gradually weakening under the far PES. At Min and Saddle positions, the charge polarization rate of the latter is faster than that of the former, and the number of charges is gradually close to each other at Z Low = 8.230 Å in Figs. 10(b) and 10(d). Moreover, the energies of both Min and Saddle are possible equivalent at Z high = 8.230 Å due to that DOSs of Min and Saddle are similar in Fig. S8 in the ESM. Thus, the equivalent interlayer electron states and electron quantities may be the key of the potential energy crossover at Min and Saddle as to inducing superlubricity behavior of P4O2.
Finally, it is worth noting that the binding energy crossing is the key of superlubricity behavior of o-BP, but not all that could produce superlubricity behavior. First, the binding energy intersection is located on MEP. Second, all Min and saddle peaks existed on MEP have to intersect at one point synchronously. The latter is a relatively harsh condition, which is a key reason why P8 and P8O do not have superlubricity behavior. In addition, the simpler PES is easier to achieve these conditions above as to obtaining the theoretical superlubricity behavior, such as P4O2 and P4O3.

Conclusions
Phosphorene is extremely susceptible to oxidation, and therefore is limited in many fields. Based on DFT calculation, o-BP exhibits the weaker interlayer adhesion than pristine BP, suggesting that it serves as solid lubrication agent potential. At zero load, the friction performance of o-BP is better than that of pristine BP. Expressly, the best friction property of P4O2 implies that one of o-BP can be adjusted through the specific oxidation. This mainly results from that the O channel with the low sliding resistance is formed on the surface of P4O2, which ensures the low sliding resistance when the upper layer O atoms enter the O channel of the lower layer O atoms. Importantly, the superlubricitiy behavior of o-BP under the non-zero load is predicted based on the flattening PES at critical load/distance induced by the binding energy crossover phenomenon. The flattening PES of o-BP is only dominated by electrostatic role under the high-load, while it is attributed to the synergistic action of both the dispersion and electrostatic role under the low-load. Distinctly, the transform from ultra-low friction to superlubricity state of BP can be achieved by critical oxidation and load. It is worth noting that not all the binding energy crossovers are able to produce superlubricitiy behavior, in which all peaks of MEP have to intersect simultaneously. In addition, negative friction behavior seems to be a general phenomenon when Z > Z min , while which cannot be explained by the conventional fold mechanism of the 2D materials due to the surfacesurface rather than tipsurface structure of o-BP. This phenomenon cannot be captured by the conventional AFM because of the jump effect with instability when Z > Z min , which may be the main reason why the current study has not been discovered experimentally. In conclusion, the application of o-BP in the friction field not only shows great potential, but also reduces its application limitations such as high vacuum, dry atmosphere, and aerospace/space (high-energy atomic oxygen).