Method for regulating and controlling black phosphorus interlayer friction by using strain-induced moire

Abstract

The invention relates to a method for regulating and controlling black phosphorus interlayer friction by using strain-induced moire. The method comprises the following steps: (1) establishing a molecular dynamics model consisting of a black phosphorus probe and a black phosphorus substrate; (2) executing simulation and processing data: (1) determining a changing curve of the instantaneous friction force along with the sliding time; (2) determining the energy absorbed by the temperature adjusting layer between the black phosphorus / black phosphorus interfaces and the average friction force of the friction interface within the biaxial strain range of 0.03-0.12; (3) determining the relationship between the atom contact state and the average friction force; (4) determining the energy absorbed by the temperature adjusting layer between the black phosphorus / black phosphorus interfaces and the average friction force of the friction interface within the relative adhesion factor range of 1-70; (5) determining the relation between the average friction force and the contact number and the number of atoms of different relative adhesion factors at different contact heights; (6) determining a fast Fourier transform spectrum corresponding to the instantaneous friction force; and (7) calculating the phonon spectrum between the probe and the substrate. According to the method, the influence of the moire patterns constructed on the surface of the substrate on the friction force between black phosphorus / black phosphorus interfaces is determined.

Description

Technical Field

[0001] The present invention relates to the field of molecular dynamics technology, and in particular to a method for regulating friction between black phosphorus layers by utilizing strain-induced moiré. Background Art

[0002] In recent years, with the rapid development of materials science and nanotechnology, two-dimensional materials have gradually become a research hotspot. Due to their unique electronic, optical, and mechanical properties, these materials are widely used in fields such as nanoelectronics, flexible electronic devices, and high-performance sensors. Among them, black phosphorus (BP), an allotrope of phosphorus, exhibits two-dimensional properties similar to materials such as graphene and molybdenum disulfide due to its layered structure. In a single layer of BP, electron mobility is very high, and the band gap can be adjusted by varying the number of layers, which holds great promise for its application in flexible electronic devices. BP also exhibits excellent mechanical properties, making it a promising material for research into tribological properties. Unlike traditional two-dimensional materials, BP's wrinkled honeycomb structure significantly influences its tribological properties, both due to its layered structure and the external environment. Generally speaking, the tribological properties of two-dimensional materials at the nanoscale are influenced by a range of factors, including temperature, sliding velocity, and interatomic adhesion.

[0003] Unlike traditional two-dimensional materials, BP's wrinkled honeycomb structure makes its tribological behavior more sensitive to its layered structure and external environmental factors. Cui et al. found that the number of layers significantly affects the friction of black phosphorus. The friction coefficient of black phosphorus sheets with fewer than five layers increases with decreasing layer number, while the friction coefficient of sheets with more than five layers approaches the bulk value. At the atomic scale, black phosphorus exhibits significant friction anisotropy, with maximum friction in the armchair direction and minimum friction in the zigzag direction. Regarding environmental factors, black phosphorus readily degrades in the atmosphere through reactions with oxygen and moisture. However, this degradation process has a positive impact on its lubricity, significantly reducing the friction coefficient and even achieving a superlubricity state. Furthermore, interfacial interactions cannot be ignored, as they not only alter the tribological properties of black phosphorus but also affect its mechanical properties, such as fracture strength and Young's modulus. These findings provide a rich understanding of the friction mechanisms of black phosphorus. They lay a theoretical foundation for its application in practical engineering and help promote technological development in related fields.

[0004] In addition, previous studies have reported that the friction of two-dimensional materials can be manipulated by moiré patterns at the friction interface. There are two approaches to controlling friction by constructing lattice-mismatched interfaces: one is to form a heterostructure between two surfaces with unequal lattice constants; the other is to rotate two contacting surfaces of a homogeneous structure with the same lattice constant relative to each other, or to apply strain, thereby creating an asymmetric friction interface. Moiré patterns not only influence the friction process but also affect their electronic properties and quantum optics, playing a significant role in the friction process. Regarding the friction of two-dimensional materials, Song et al. experimentally demonstrated structural superlubricity at the microscopic scale for heterojunctions between single-crystal graphite and hexagonal boron nitride. Atomistic simulations revealed that the friction mechanism in heterojunctions is primarily derived from out-of-plane atomic fluctuations generated by soliton-like moiré superstructure motion. Bao et al. believe that the reconstruction and deformation of the moiré pattern is determined by the competition between intralayer strain and interlayer coupling, and that the friction force during sliding heterogeneous bilayers is more likely to fall within the superlubricity range. Tang et al. theoretically explained the friction energetics of moiré patterns in twisted systems, established a clear connection between them and potential energy ripples, and reconfirmed in dynamic friction that friction comes more from the edges than from the center, emphasizing the importance of moiré patterns.

[0005] Numerous studies have examined the effects of strain and strain-induced moiré on friction. Researchers have achieved ultralow friction in graphene / graphene systems by applying prestrain to graphene substrates. The effect of applied strain on friction is minimal when the lattice constants at the interface are different. Zhou et al. found that applying biaxial and uniaxial strain to hexagonal graphene sheets and rectangular SLMoS2 systems resulted in little change in interlayer friction. Lin et al. observed graphene / graphene friction under substrate-strained conditions and found that friction did not change much with strain when the contact interface was non-commensurate. Peng et al. observed that applying biaxial and uniaxial strain to hydrogenated graphene gradually reduced atomic-level roughness. Furthermore, this strain-induced friction reduction was robust over a wide range of comparability, load, and dimensional parameters. Regarding the effect of strain-induced moiré on friction, researchers also found that some atoms in the strain-induced moiré region have positive friction, while others have negative friction. These two atomic forces cancel each other out, resulting in ultralow overall friction. Similarly, Wang et al. applied biaxial strain to the graphene substrate in a graphene / graphene system and found that the friction force could be reduced, especially when the probe size was a multiple of the moiré period length, the friction force would periodically reach the lowest friction.

[0006] In summary, previous studies have all achieved ultra-low friction by applying strain to create a lattice mismatch between the sliding probe and substrate. However, sometimes it is necessary to increase friction to serve people's lives and industrial production. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a method for regulating the friction between black phosphorus layers by utilizing strain-induced moiré.

[0008] To solve the above problems, the present invention provides a method for regulating the friction between black phosphorus layers using strain-induced moiré, comprising the following steps:

[0009] ⑴ Establish a molecular dynamics model consisting of black phosphorus probe and black phosphorus substrate:

[0010] The substrate comprises a rigid support layer, a temperature regulating layer and a free motion layer; fixed layers are respectively provided on both sides of the top of the rigid support layer, and a temperature regulating layer is provided on the inner side of each fixed layer; a free motion layer is provided between the two temperature regulating layers;

[0011] Each atom of the probe is equipped with springs in the x, y, and z directions. The x-direction spring drives the probe to slide at a constant speed of 8 m / s. The y-direction spring prevents the probe from rotating around the z-axis and translating along the y-axis during sliding. The z-direction spring applies a normal load and prevents the probe from translating along the z-axis.

[0012] A periodic boundary condition is set in the x direction of the substrate, and free boundary conditions are set in the y and z directions;

[0013] ⑵Execute simulation and process data:

[0014] ① Determine the curves of instantaneous friction force versus sliding time when the relative adhesion factors are 1 and 40, and the biaxial strains are 0.05 and 0.08 respectively;

[0015] ② Determine the energy absorbed by the thermoregulatory layer at the black phosphorus / black phosphorus interface and the average friction force at the friction interface when the relative adhesion factors are 1, 5, 40, and 60 at 0K and the relative adhesion factor is 40 at 300K and the biaxial strain is in the range of 0.03 to 0.12;

[0016] ③ Based on the contact distance under initial conditions, the relationship between the average friction force and the number of contacts when the relative adhesion factors are 1 and 40, respectively, is explored. By counting the number of atoms with different strains at different contact heights, the relationship between the atomic contact state and the average friction force in the friction system is determined.

[0017] ④ Determine the variation curve of instantaneous friction force with sliding time when the biaxial strain is 0.06 and the relative adhesion factor is 30 and 70, respectively, and the corresponding substrate moiré pattern; determine the energy absorbed by the thermoregulatory layer at the black phosphorus / black phosphorus interface and the average friction force of the friction interface when the biaxial strain is 0.06, 0.08, and 0.1 at 0K, and when the biaxial strain is 0.06 at 300K, and the relative adhesion factor is in the range of 1 to 70;

[0018] ⑤ Determine the relationship between the average friction force and the number of contacts when the biaxial strain is 0.08, as well as the number of atoms with different relative adhesion factors at different contact heights;

[0019] ⑥ Determine the fast Fourier transform spectrum corresponding to the instantaneous friction force when the relative adhesion factors are 50 and 60 and the biaxial strains are 0.08 and 0.11;

[0020] ⑦ When the relative adhesion factors are 50 and 60, and the biaxial strains are 0.08 and 0.11, the phonon spectra between the probe and the substrate are calculated.

[0021] The simulation and data processing in step (2) also includes: calculating a single moiré period for the corresponding base moiré pattern under different working conditions, so as to determine the influence of the moiré pattern on the instantaneous friction force during the friction process.

[0022] The simulation and data processing performed in step (2) also include: when the relative adhesion factor is 1 and the biaxial strain is 0.03, the contact distance is calculated from the lowest height of the moiré pattern of the phosphorus atoms in the uppermost layer of the substrate and the average trajectory height of the probe during the sliding process; the contact distance is divided into a strong contact area and a weak contact area according to different heights, and it is determined that the atoms in the strong contact area have a greater influence on friction.

[0023] The simulation and data processing performed in step (2) also includes: analyzing the fast Fourier spectrum under different relative adhesion factors and strains, finding the energy dissipation channels caused by three washboard frequencies: moiré washboard frequency, strain washboard frequency, and traditional stick-slip washboard frequency, as well as schematic diagrams of the three washboard frequencies.

[0024] The simulation and data processing in step (2) also include: using 16 atoms in the selected area to calculate the number of phonons of the black phosphorus / black phosphorus interface probe and the substrate, and verifying the influence of three washboard frequencies, namely moiré washboard frequency, strain washboard frequency and traditional stick-slip washboard frequency, on friction by analyzing the number of phonons; and calculating the ratio of the energy dissipation excited at each washboard frequency to the total energy dissipation to explore the contribution degree.

[0025] Compared with the prior art, the present invention has the following advantages:

[0026] 1. The present invention calculates the interfacial friction during the friction process by running the established molecular dynamics model under different relative adhesion factors and different strains, and then processes and analyzes it to determine the influence of the moiré pattern of the substrate surface structure on the friction between the black phosphorus / black phosphorus interface.

[0027] 2. The present invention quantitatively analyzes the changes in friction through the number of atomic contacts and the contact quality of the friction interface, clarifies the mechanism of the influence of contact quality on friction force, and further provides theoretical guidance for the influence of moiré patterns between friction interfaces on the friction between black phosphorus layers.

[0028] 3. By analyzing the fast Fourier spectrum of instantaneous friction force under different working conditions, the present invention discovered the friction dissipation channels caused by three washboard frequencies (i.e., moiré washboard frequency, strain washboard frequency, and traditional stick-slip washboard frequency), and further verified the influence of the three dissipation channels on friction through phonon spectrum. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0030] Figure 1 This is a molecular dynamics model of an embodiment of the present invention.

[0031] Figure 2 The instantaneous friction force and moiré pattern of different strains under the relative adhesion factor conditions in the embodiment of the present invention are shown in FIG. Where: a is λ=1, ε xx =ε yy = 0.05 and 0.08 instantaneous friction force and sliding distance; b is the instantaneous friction force within the red line range; c and d are when λ = 1, ε xx =ε yy = 0.05 and 0.08 of the upper atomic height map; when e is λ = 40, ε xx =ε yy = 0.05 and 0.08, the relationship between the instantaneous friction force and the sliding distance; f is the instantaneous friction force within the corresponding red line range; g and h are when λ = 40, ε xx =ε yy = 0.05 and 0.08 of the atomic height map of the substrate.

[0032] Figure 3 Graph showing average friction force as a function of strain at different relative adhesion factors and temperatures in an embodiment of the present invention.

[0033] Figure 4 Schematic diagram of the contact distance model and the friction behavior under different strain and relative adhesion factors in the embodiment of the present invention. xx =ε yy Schematic diagram of the contact distance between the black phosphorus layer on the substrate and the probe when L = 0.03, 0.03 =15.03nm; b and d are the variations of average friction force and contact area with strain when λ=1 and 40; c and e are the height area distribution diagrams of contact area under different strains when λ=1 and 40.

[0034] Figure 5 Figures 1 and 2 show the instantaneous friction distribution curves and moiré patterns as λ varies with the same strain, as well as the average friction curves at different temperatures, for an embodiment of the present invention. Figures a and b show the relationship between the instantaneous friction force and the sliding distance at λ = 30 and 70°; b shows the instantaneous friction force within the red line in Figure (a); c shows the moiré pattern cloud at λ = 30°; d shows the moiré pattern cloud at λ = 70°; and e shows the average friction force as λ varies at the same strain at 0K and 300K.

[0035] Figure 6 The friction behavior under different λ values ​​in the embodiment of the present invention is shown in FIG. Where: a is ε xx =ε yy =0.06; b is the height distribution of the contact area under different λ.

[0036] Figure 7 Figure 1 is a schematic diagram of the fast Fourier transform (FFT) of different contact states and the internal mechanism causing the three dissipation channels in the embodiment of the present invention. Among them: a, b, c and d are the friction FFT spectra under different strain and relative adhesion factors; e is a schematic diagram of the substrate moiré pattern, L ε is the period length of the moiré pattern; f is the AB stack of two layers of black phosphorus on the substrate. t m (green), f t ε (cyan), f t (blue) are the moiré washboard frequency, strain washboard frequency, and washboard frequency, respectively.

[0037] Figure 8 is the quantitative analysis of the probe atom excited phonons and the energy dissipation ratio at each washboard frequency peak in the embodiment of the present invention, v s =8m / s. Where: a and b are ε xx =ε yy = 0.08, λ = 50 and 60; c and d are ε xx =ε yy = 0.11, λ = 50 and 60; e is ε xx =ε yy =0.08, 0.11 and λ = 50, 60, the energy dissipation ratio corresponding to the three washboard frequency peaks. t m (green), f t ε (cyan), f t (Orange) are the moiré washboard frequency, strain washboard frequency, and washboard frequency, respectively.

[0038] Figure 9is the change of potential barrier under different relative adhesion factors and strains in the embodiment of the present invention. Where: a and b are ε xx =ε yy = 0.05 when λ = 1 and 40; c and d are ε xx =ε yy = 0.08 when λ = 1 and 40.

[0039] Figure 10 The high area distribution of atoms under different working conditions in the embodiment of the present invention. Wherein: a and b are the high area distribution of atoms under different strains of λ = 1 and 40; c is the DCR / SCR dividing point of 4.3 under λ = 1 and different strains; d is the DCR / SCR dividing point under ε xx =ε yy =0.08 and different relative adhesion factors, the DCR / SCR cut-off point is 4.1. DETAILED DESCRIPTION

[0040] A method for regulating friction between black phosphorus layers using strain-induced moiré patterns comprises the following steps:

[0041] ⑴ Establish a molecular dynamics model consisting of black phosphorus probe and black phosphorus substrate:

[0042] The base includes a rigid support layer, a temperature adjustment layer and a free motion layer; fixed layers are respectively provided on both sides of the top of the rigid support layer, and a temperature adjustment layer is provided on the inner side of each fixed layer; a free motion layer is provided between the two temperature adjustment layers.

[0043] Each atom of the probe is equipped with springs in the x, y, and z directions. The spring in the x direction drives the probe to slide at a constant speed of 8 m / s. The spring in the y direction prevents the probe from rotating around the z axis and translating along the y axis during sliding. The spring in the z direction applies a normal load and prevents the probe from translating along the z axis.

[0044] Periodic boundary conditions are set in the x-direction of the substrate, and free boundary conditions are set in the y and z-directions.

[0045] ⑵Execute simulation and process data:

[0046] ① Determine the curves of instantaneous friction force versus sliding time when the relative adhesion factors are 1 and 40, and the biaxial strains are 0.05 and 0.08 respectively;

[0047] ② Determine the energy absorbed by the thermoregulatory layer at the black phosphorus / black phosphorus interface and the average friction force at the friction interface when the relative adhesion factors are 1, 5, 40, and 60 at 0K and the relative adhesion factor is 40 at 300K and the biaxial strain is in the range of 0.03 to 0.12;

[0048] ③ Based on the contact distance under initial conditions, the relationship between the average friction force and the number of contacts when the relative adhesion factors are 1 and 40, respectively, is explored. By counting the number of atoms with different strains at different contact heights, the relationship between the atomic contact state and the average friction force in the friction system is determined.

[0049] ④ Determine the variation curve of instantaneous friction force with sliding time when the biaxial strain is 0.06 and the relative adhesion factor is 30 and 70, respectively, and the corresponding substrate moiré pattern; determine the energy absorbed by the thermoregulatory layer at the black phosphorus / black phosphorus interface and the average friction force of the friction interface when the biaxial strain is 0.06, 0.08, and 0.1 at 0K, and when the biaxial strain is 0.06 at 300K, and the relative adhesion factor is in the range of 1 to 70;

[0050] ⑤ Determine the relationship between the average friction force and the number of contacts when the biaxial strain is 0.08, as well as the number of atoms with different relative adhesion factors at different contact heights;

[0051] ⑥ Determine the fast Fourier transform spectrum corresponding to the instantaneous friction force when the relative adhesion factors are 50 and 60 and the biaxial strains are 0.08 and 0.11;

[0052] ⑦ When the relative adhesion factors are 50 and 60, and the biaxial strains are 0.08 and 0.11, the phonon spectra between the probe and the substrate are calculated.

[0053] The present invention also includes performing simulation and processing data:

[0054] For the corresponding base moiré patterns under different working conditions, a single moiré period is calculated to determine the influence of the moiré pattern on the instantaneous friction force during the friction process.

[0055] When the relative adhesion factor is 1 and the biaxial strain is 0.03, the contact distance is calculated from the lowest height of the moiré pattern of phosphorus atoms in the top layer of the substrate and the average trajectory height of the probe during sliding; the contact distance is divided into strong contact areas and weak contact areas according to different heights, and it is determined that the atoms in the strong contact area have a greater impact on friction.

[0056] By analyzing the fast Fourier spectrum under different relative adhesion factors and strains, we found the energy dissipation channels caused by three washboard frequencies: moiré washboard frequency, strain washboard frequency, and traditional stick-slip washboard frequency, as well as schematic diagrams of the three washboard frequencies.

[0057] Sixteen atoms in the selected area were used to calculate the number of phonons at the black phosphorus / black phosphorus interface probe and the substrate. The effects of three washboard frequencies, namely moiré washboard frequency, strain washboard frequency and traditional stick-slip washboard frequency, on friction were verified by analyzing the number of phonons. The ratio of the excited energy dissipation to the total energy dissipation at each washboard frequency was calculated to explore the degree of contribution.

[0058] Example

[0059] This paper uses a black phosphorus / black phosphorus friction system as the research object and explores the research method of controlling friction force by strain-induced moiré. The specific process is as follows:

[0060] 1. Establish molecular dynamics model

[0061] like Figure 1 Shown is a model system for studying friction between BP layers, in which a square BP probe slides on a rectangular BP substrate. Biaxial strain is applied to the bottom layer of the substrate. After the strain is applied, the lattice constants of the two substrate layers differ, resulting in periodic moiré patterns on the substrate surface. The initial dimensions of the tip are 19.6 × 18.4 nm. 2 (9680 atoms), initial strain (ε xx =ε yy =0) the substrate size is 19.6×41.4nm 2 (42464 atoms). The atoms at the edge of the contact area in the y direction (non-sliding direction) and the bottom layer of the substrate are fixed to simulate the constraints imposed by the rigid support in the experiment. The atoms on both sides of the fixed layer are Berendsen thermostats. In order to eliminate the influence of temperature on phonons, only excited phonons at a temperature of 0K are considered. The time step of the friction process is set to 0.0005ps, which is lower than the fastest time for phonon annihilation, so as to obtain stable friction information. 200,000 steps are run to reach the initial equilibrium state of the system, and the subsequent sliding process is run for 1.2 million steps. In order to slide precisely in the specified direction, each atom at the tip is subjected to a spring in the x, y and z directions, and a spring stiffness of 10,000nN / nm is applied in each direction. In the sliding direction, that is, the x direction, the spring on allows the probe to move at a speed of v s Slide, where v s = 8 m / s. Springs in the remaining two directions constrain the atoms' translation and rotation. Furthermore, a periodic boundary condition is defined in the x-direction, while free boundary conditions are defined in the y- and z-directions. Therefore, the atoms between the probe and substrate always mutually excite each other in the x-direction.

[0062] To study the effect of the adhesion properties between the strained layer below the substrate and the unstrained layer above it on the moiré pattern, the present invention utilizes Lennard-Jones (LJ) potentials with different interaction strengths between the probe and the substrate, and between the substrate and the layers. The Stillinger-Weber (SW) potential is used for all interactions between atoms within the layer, while the LJ-1 potential is used to describe the atomic interactions between the probe and the substrate; the cutoff radius r c=0.8938nm, the potential well depth between the probe and the substrate layer ε1 = 15.94meV, and the equilibrium constant σ1 = 0.3438nm. In addition, LJ-λ is used to describe the atomic interaction between the two layers of the substrate, and the potential well depth ε λ =λε1, equilibrium constant σ λ = σ1, where λ is the relative adhesion factor representing the ratio of substrate-to-substrate adhesion strength. The critical axial strains of a monolayer of BP in the zigzag and armrest directions are 27% and 30%, respectively, and can withstand stresses of 18 GPa and 8 GPa. In the simulations presented here, due to computational resources and the size of the corrugated pattern, the biaxial tensile strain of the underlying substrate was gradually increased from 0.03 to 0.12, which is within a safe range.

[0063] Each simulation was performed using LAMMPS software.

[0064] 2. Analyze the effect of moiré on the friction between BP layers under the same λ variation with strain

[0065] (1) Calculate the curve of instantaneous friction force changing with strain through spring force

[0066] based on Figure 1 The friction model established in [1] was used to investigate the correlation between strain-induced moiré patterns between substrate layers and friction characteristics. The instantaneous friction force was obtained by measuring the spring force in the x-direction of the probe, and the average friction force was then determined by calculating the time-dependent average.

[0067] Figure 2 (a) shows the relationship between instantaneous friction force and sliding distance at different strains when λ = 1. Regular stick-slip behavior is observed at both strains. Further observation reveals that the instantaneous friction force exhibits a long-periodic variation, distinct from the stick-slip phenomenon, and that the long period gradually shortens as the strain increases.

[0068] Figure 2 (b) is a zoomed-in image of a long-period instantaneous friction force. In this friction model, in addition to the influence of the substrate surface atoms on the probe, the substrate moiré also has an impact. Therefore, it is speculated that the long-periodicity of the instantaneous friction force over the sliding distance may be caused by the substrate moiré.

[0069] According to the atomic height map of the substrate layer that can show moiré patterns, such as Figure 2 (c) and (d), calculate the moiré period L of the substrate ε , and found that Figure 2 The long period in (a) is the same (where L 0.05 =9.3nm, L 0.09 =6.2nm). Therefore, there is not only stick-slip phenomenon but also moiré stick-slip phenomenon in the instantaneous friction force. Figure 2 (e) is the relationship curve between the instantaneous friction force and sliding distance for two strains under the condition of λ=40. The stick-slip phenomenon and long-period moiré stick-slip phenomenon are also found. Figure 2 (g) and (f) are the corresponding moiré patterns.

[0070] pass Figure 2 (a) and (c) show that as strain increases, the instantaneous friction force peak decreases from 154nN to 136nN at λ = 1, and increases from 77nN to 93nN at λ = 40. To further understand these two different trends in friction change, the effect of strain change on the average friction force was further statistically analyzed.

[0071] (2) Curves of variation with strain under different relative adhesion factors

[0072] Figure 3 The curves showing the variation of average friction with strain for different relative adhesion factors and temperatures are shown. It can be seen from the figure that at 0 K, the average friction changes with increasing relative adhesion factor. When λ = 1, the average friction gradually decreases with increasing strain. Furthermore, as the relative adhesion factor increases, the average friction tends to level off with increasing strain at λ = 5. At larger relative adhesion factors, such as λ = 40 or 60, the average friction increases with increasing strain. The average friction calculated at 300 K shows that temperature changes do not affect the monotonic variation of friction.

[0073] exist Figure 2 (c)-(d) and Figure 2 In (g)-(h), the moiré pattern in the lower layer of the substrate changes depending on the strain and interlayer force. Previous research has shown that the actual contact area between two contacting interfaces influences friction, and an increase in friction can be attributed to the increased contact area. Therefore, a contact distance can be defined to discuss the effect of moiré on the contact area of ​​the friction interface.

[0074] (3) Relationship between contact quantity and contact quality under different strains

[0075] Figure 4 (a) is a side view of the upper substrate and the probe under the initial working condition. The arrow on the upper substrate indicates the atomic force in the z direction, which can be used to characterize the moiré height, L 0.03 is a complete moiré cycle under this strain. The distance between the lowest height of the moiré of phosphorus atoms on the upper substrate and the average sliding track height of the probe is defined as the contact distance between the substrate and the probe, and is obtained as The substrate atoms within this contact distance are considered to be in contact with the probe, and the smaller the value, the closer the contact.

[0076] The present invention counts the number of substrate atoms m in contact with the probe, and obtains the probe-substrate contact area according to the formula S=ms, where s is the contact area of ​​a single P atom (the contact area of ​​each atom is ). The actual contact area is recorded as the number of contacts. When λ = 1, Figure 4 As shown in (b), the trend of average friction with strain is similar to that of the number of contacts, but the slopes of their dependence on strain are clearly different, with the average friction decreasing more rapidly. Therefore, it can be concluded that the change in the number of contacts cannot fully explain the change in friction, and that another mechanism plays a major role.

[0077] Previous studies have found that the main reason for friction enhancement under the same contact area is the improvement of contact quality. At the same time, it was found that the density and strength of the pinning points increased during the strengthening stage. Not all atoms in the actual contact area contribute to the friction force. The atoms with contact quality are the ones that mainly affect the friction force. Since the degree of atomic nesting is different at different contact heights, this paper quantitatively calculates the The number of atoms in contact within each distance range.

[0078] Depend on Figure 4 (c) can be found in The number of atoms inside the tube gradually increases, which is opposite to the trend of the average friction force. The number of atoms decreases sharply with the increase of strain, which shows that The number of atoms in the contact is strong, The effect within the friction zone is weak. Therefore, these two regions are defined as the strong contact region (DCR) and the weak contact region (SCR). This explains why the average friction force decreases rapidly even if the decrease in the number of contacts is small, precisely because the contact quality decreases significantly in the DCR.

[0079] besides, Figure 4 (d) also counts the case of λ = 40, and finds that the number of contacts is large when the strain is 0.03. At the strain of 0.06 to 0.12, the change in the average friction force is larger than the number of contacts. The number of atoms in contact at different distances. Figure 4 In (e), as in the case of λ=1, The trend of the number of atoms is opposite to the trend of the average friction. The trend in the number of atoms is the same as the trend in the average friction. Applying the findings from λ = 1 to λ = 40, we find that although the number of atoms in the SCR at a strain of 0.03 is large, their contribution to friction is small, resulting in a very low average friction at a strain of 0.03. In the DCR, as the strain increases, the number of atoms increases, the contact mass increases, and the increase is large, resulting in a relatively large change in the average friction. This once again confirms that the DCR / SCR division is reasonable, with the atoms in the DCR contributing strongly and the atoms in the SCR contributing weakly.

[0080] In addition, the present invention also attempts different DCR / SCR regions to verify the rationality of this division. In the present invention, the ripple pattern caused by pre-strain can be understood as regular wrinkles, so the atoms within the contact distance d can be divided according to different contact distances with the tip.

[0081] In the present invention, select As the cutoff point to explore the change of atomic height. Figure 4 (c) It can be seen that the change trend of atoms in DCR is the same as that of average friction, and the change slope is much greater than the change slope of contact area. In addition, it is found that The area of ​​​​is opposite to the friction change trend. At this time, under different relative adhesion factors, this trend is confirmed, such as Figure 4 (e). Therefore, The contact distance is the dividing line, select The area is regarded as the shallow contact area, The area is regarded as the deep contact area.

[0082] For the division of contact area, the following are given: and The atomic height distribution as the DCR / SCR cutoff point. Figure 10 In (a) and (b), it can be found that the change of the number of atoms with the increase of strain is related to the average friction force at the contact distance. The change in the area where the transformation occurs is the same as that in Therefore, choose 4.1, 4.2 and As the dividing point of DCR / SCR, it is explored. Figure 10 (c) shows that As the cutoff point, the atomic height distribution at λ = 1 is plotted. The atomic change trend at is opposite to the average friction change trend. By calculating the overall atomic change in DCR, it is found that it has a decreasing trend, but the decrease is small, which is consistent with the Figure 4 The contact area changes in (b) are the same. Figure 10 (d) When When ε is the cutoff point, it can be found thatxx =ε yy = 0.08, the overall atomic change trend in DCR is Figure 4 The average friction in (d) shows an opposite trend.

[0083] Therefore, from the perspective of atomic change trend, the choice The DCR / SCR cutoff point is correct. This method explores the mechanism affecting friction at a deeper level from the atomic level and provides a new approach for subsequent research on BP material friction.

[0084] (4) Calculate the instantaneous friction force over time using the spring force

[0085] The previous study compared the changes in instantaneous friction force under different strains with the same λ and found that the atomic stick-slip period is longer when λ = 1 than when λ = 40. Previous research has shown that friction is greater when there is a multi-slip effect. Therefore, a comparison was conducted under the same strain but different λ conditions.

[0086] like Figure 5 As shown in (a) and (b), the molar stick-slip phenomenon is more obvious at a relatively large λ, and the molar stick-slip phenomenon period is Figure 5 The periods in (c) and (d) are the same. It can also be seen that as λ increases, the minimum peak value of the instantaneous friction force decreases from -72nN to -94nN.

[0087] In order to explore the main reasons affecting friction, Figure 5 (e) The effect of the change of λ at different temperatures on the average friction force is statistically analyzed, and it is found that the average friction force decreases with the increase of λ. At 0K, the change of the average friction force with the increase of strain at λ = 1 and the intersection with Figure 3 The trend is consistent. Figure 3 As can be seen from the figure, since the average friction force fluctuates within a certain range at λ = 5, Figure 5 Crossover at λ = 5 in (e).

[0088] 3. Analyze the effect of moiré on the friction between BP layers under the same strain and λ variation

[0089] Figure 6 The average friction force shown in (a) has the same changing trend as the number of contacts, and the former has a larger change amplitude. Figure 5 From (c) and (d), we can see that the increase of λ leads to a deeper nesting of the base atoms. Figure 6 (b) DCR The number of atoms in the The number of atoms in the SCR decreases more slowly and plays a smaller role. Therefore, the rapid decrease in contact mass leads to a greater decrease in average friction.

[0090] Furthermore, the difference in friction can be attributed to the change in the interfacial potential barrier, which is determined by the difference between the maximum and minimum van der Waals potentials between the layers. Figure 9 The changes of potential barrier and relative adhesion factor under different strains are shown. xx =ε yy = 0.05, 0.08, when λ increases from 1 to 40, the potential barrier decreases. Figure 9 In (a) and (c), when λ = 1, the potential barrier decreases with increasing strain. Figure 9 In (b) and (d), when λ = 40, the barrier increases with strain. The change of the total barrier height under different strains and relative adhesion factors is similar to Figure 3 The variation of the average friction force in is consistent with that in . Figure 9 The potential barrier in Figure 2 Same long period oscillation.

[0091] 4. Using the washboard frequency in the FFT spectrum and the number of phonons excited by the probe and substrate surfaces, quantitatively study the differences in friction and energy dissipation between BP layers

[0092] (1) Fast Fourier transform spectra under different strains and relative adhesion factors revealed three energy dissipation channels caused by washboard frequencies

[0093] During the entire friction process, the work done by friction is eventually converted into heat, which indicates that friction is actually an energy conversion process, making energy dissipation a key scientific issue in understanding friction. When the BP probe slides on the substrate, the relative motion between the contact interfaces stimulates the atoms on the surface to move at the washboard frequency f during the stick-slip process. t =v s / 2(a+b), where 2(a+b) is the lattice period length in the Armchair direction (e.g. Figure 7 (f) The green-blue black phosphorus layer is the unstrained base layer. a and b refer to the projected lengths of the bond lengths between phosphorus atoms on the xy plane. ), at this time we get the washboard frequency f t = 0.0181 THz. The energy of the friction system is converted into mechanical vibrations at different frequencies and gradually dissipated into heat as a dissipation channel.

[0094] To investigate whether moiré patterns induce interfacial vibrations that differ from stick-slip vibrations and, therefore, whether different energy dissipation channels are generated, thereby affecting friction, we performed a fast Fourier transform (FFT) on the instantaneous friction force under different strains and λ values. Here, the FFT of the instantaneous spring force is the FFT of the probe displacement, meaning that the FFT spectrum actually represents the probe's vibration frequency and amplitude. Figure 7(a) and (b) represent ε xx The FFT spectrum at different λ values ​​is 0.08, where the green reference line perfectly corresponds to the washboard frequency calculated from the moiré period length, i.e., the moiré washboard frequency f t m =v s / L ε , the moiré period length L ε Schematic diagram corresponding Figure 7 In (e), we can get the moiré washboard frequency equal to 0.00129 THz when the strain is 0.08. In addition, the first peak of the blue reference line also perfectly corresponds to the washboard frequency f calculated from the BP lattice period length. t . And in addition to its first peak, 2 times, 3 times f t The peak at can also be easily distinguished in the FFT spectrum. The obvious peak in the FFT spectrum indicates that the washboard frequency and its harmonic components have the main contribution to the friction force.

[0095] Likewise, Figure 7 (c) and (d) represent ε xx The FFT spectrum of different λ values ​​when the strain is 0.11 shows the same pattern as that of 0.08 strain, where f t m 、f t =0.00180THz and 0.0181THz respectively. In addition to the influence of moiré and the original lattice, there is also a washboard frequency in friction that is excited by the lattice period length of the applied strain, which is defined as the strain washboard frequency f t ε .like Figure 7 (f) The blue-blue black phosphorus layer is the strained underlying substrate, and the lattice period length of the strain applied is 2(a+b) / (1+ε xx ). Through the formula f t ε =v s / 2(a+b)(1+ε xx )The calculated frequency is also consistent with Figure 7 The main peaks in (a)-(d) correspond to each other, with the strain washboard frequencies corresponding to strains of 0.08 and 0.11 being 0.0168 THz and 0.0163 THz, respectively, and their multiple harmonics also perfectly correspond. This means that in the case of friction caused by moiré patterns due to pre-strain in the lower layer of the substrate, there are three friction dissipation channels that couple together to affect friction.

[0096] (2) Determine the effect of the number of phonons at different washboard frequencies on the friction force and the contribution of each washboard frequency

[0097] Research has shown that when friction converts energy into heat, energy dissipation channels between contacting surfaces transfer energy at the friction interface in the form of phonons. To quantitatively analyze the effect of excitation frequency on energy dissipation under varying excitation amplitudes and repeatability, the present study calculated the number of excited phonons during the oscillation process.

[0098] It is well known that the frequency pattern of friction-excited phonons in the black phosphorus layer during commensurate contact perfectly matches the washboard frequency of the probe-substrate atoms and its harmonics. Furthermore, since changes in friction are primarily determined by the excitation and dissipation of low-frequency phonon modes, changes in the number of low-frequency phonons can reflect changes in friction.

[0099] Figure 8 (a)-(d) show the number of phonons under different strains and different λ. The phonons are mainly distributed in the f of the BP probe. t m 、f t ε 、f t At these three excitation frequencies, it is verified again that the three dissipation channels found in the FFT spectrum do participate in and affect the friction force. t ε 、f t Harmonic, f t m Phonon dissipation also occurs at the harmonics, and f t m The number of phonons at increases with the increase of strain, and the number of harmonics increases with the increase of λ, which proves that the moiré period contributes to the friction force.

[0100] Under the same strain, as λ increases, f t ε 、f t The number of phonons at its harmonics is decreasing, resulting in a decrease in energy dissipation. t m The number of phonons at its harmonics increases (this is because the BP moiré pattern is more deeply nested as λ increases), but f t m There is no increase in the number of phonons at f t 、f t ε The amplitude decreases quickly, so the friction decreases. At the same λ, as strain increases, the number of phonons at these three frequencies increases, leading to increased energy dissipation and increased friction. This further confirms that the excitation and dissipation of phonons in phonon modes determine the change in friction.

[0101] By calculating the energy dissipation and total energy dissipation at three washboard frequencies, it can be found that the change in total energy dissipation can be used to study the change in average friction. Since phonon energy dissipation mainly occurs at the frequency and its sub-peak, the dissipation at other frequencies is not considered.

[0102]

[0103] Where n is the number of phonons at each peak of the washboard frequency, is the approximate Planck constant, ω i are three washboard frequencies (i is the i-th peak).

[0104] The energy dissipation at the primary and secondary peaks of each washboard frequency was quantified according to formula (1), and the friction changes under the three dissipation channels were analyzed.

[0105] Table 1 shows the energy dissipation and total energy dissipation at the three washboard frequencies. The energy dissipation at each washboard frequency is the sum of the energy dissipation of the primary and secondary peaks. The total energy dissipation is the sum of the energy dissipation at the three washboard frequencies.

[0106] Table 1 Energy dissipation and total energy dissipation at three washboard frequencies

[0107]

[0108] It can be seen from Table 1 that when λ=50 (or 60) and the strain increases from 0.08 to 0.11, the energy dissipation generated at the moiré washboard frequency, the strain washboard frequency and the traditional stick-slip washboard frequency increases. In this case, the total energy dissipation increases and the average friction increases. When the strain is 0.08 (or 0.11) and the relative adhesion factor increases from 50 to 60, the energy dissipation generated at the friction washboard frequency increases, the energy dissipation generated at the strain washboard frequency decreases, and the energy dissipation generated at the traditional stick-slip washboard frequency decreases. At this time, the energy dissipation of 3.59E-21J (or 1.86E-20J) increased at the moiré washboard frequency is less than the energy dissipation of 7.78E-20J (or 3.76E-20J) decreased at the other two washboard frequencies. That is, when λ increases, the total energy dissipation decreases, and the average friction decreases at this time. This result is consistent with Figure 8 The results of analyzing the phonon number variation with friction are the same as those in .

[0109] In order to explore the contribution of the three energy dissipation channels in this case, the energy dissipation ratio is further used to express it. Figure 8 As shown in (e), the green column is E moire / E total , the blue column is E strain / E total , the red column is E stick-slip / E totalAs can be seen from the figure, the energy dissipation ratio is the largest at the strain washboard frequency, that is, the contribution to energy dissipation is the largest. The energy dissipation ratio at this time increases with increasing strain and decreases with increasing λ. The energy dissipation ratio at the traditional stick-slip washboard frequency is slightly smaller and decreases with increasing strain and λ. Here, the energy dissipation ratio increases with increasing strain and decreases with increasing λ. The energy dissipation ratio at the moiré washboard frequency is the smallest and increases with increasing strain and λ.

[0110] By studying total energy dissipation and its variations at various washboard frequencies, we found that three dissipation channels contribute to friction throughout the friction process. The strain washboard frequency contributes the most, and is the dominant factor; the traditional stick-slip washboard frequency contributes the second most, and the moiré washboard frequency contributes the least.

Claims

1. A method for regulating interlayer friction of black phosphorus using strain-induced moiré, comprising the following steps: ⑴ Establish a molecular dynamics model consisting of black phosphorus probe and black phosphorus substrate: The substrate comprises a rigid support layer, a temperature regulating layer and a free motion layer; fixed layers are respectively provided on both sides of the top of the rigid support layer, and a temperature regulating layer is provided on the inner side of each fixed layer; a free motion layer is provided between the two temperature regulating layers; Each atom of the probe is x 、 y 、 z Springs are provided in three directions; among them: x The spring in the direction will drive the probe to slide at a constant speed of 8m / s; y The spring in the direction is used to prevent the probe from winding during the sliding process. z Axis rotation and along y Axis translation, z The spring in the direction of the probe is used to apply the normal load and prevent the probe from moving along the z Axis translation; The substrate x Set periodic boundary conditions in the direction, y and z Set free boundary conditions in the direction; ⑵Execute simulation and process data: ① Determine the curves of instantaneous friction force versus sliding time when the relative adhesion factors are 1 and 40, and the biaxial strains are 0.05 and 0.08 respectively; ② Determine the energy absorbed by the thermoregulatory layer at the black phosphorus / black phosphorus interface and the average friction force at the friction interface when the relative adhesion factors are 1, 5, 40, and 60 at 0K and 40 at 300K, respectively; ③ Based on the contact distance under initial conditions, the relationship between the average friction force and the number of contacts when the relative adhesion factors are 1 and 40, respectively, is explored. By counting the number of atoms with different strains at different contact heights, the relationship between the atomic contact state and the average friction force in the friction system is determined. ④ Determine the variation curve of instantaneous friction force with sliding time when the biaxial strain is 0.06 and the relative adhesion factor is 30 and 70, respectively, and the corresponding substrate moiré pattern; determine the energy absorbed by the thermoregulatory layer at the black phosphorus / black phosphorus interface and the average friction force of the friction interface when the biaxial strain is 0.06, 0.08, and 0.1 at 0K, and when the biaxial strain is 0.06 at 300K, and the relative adhesion factor ranges from 1 to 70; ⑤ Determine the relationship between the average friction force and the number of contacts when the biaxial strain is 0.08, as well as the number of atoms with different relative adhesion factors at different contact heights; ⑥ Determine the fast Fourier transform spectrum corresponding to the instantaneous friction force when the relative adhesion factors are 50 and 60 and the biaxial strains are 0.08 and 0.11; ⑦ When the relative adhesion factors are 50 and 60, and the biaxial strains are 0.08 and 0.11, the phonon spectra between the probe and the substrate are calculated.

2. The method for regulating interlayer friction of black phosphorus using strain-induced moiré according to claim 1, characterized in that: The simulation and data processing in step (2) also includes: calculating a single moiré period for the corresponding base moiré pattern under different working conditions, so as to determine the influence of the moiré pattern on the instantaneous friction force during the friction process.

3. The method for regulating interlayer friction of black phosphorus using strain-induced moiré according to claim 1, characterized in that: The simulation and data processing performed in step (2) also include: when the relative adhesion factor is 1 and the biaxial strain is 0.03, the contact distance is calculated from the lowest height of the moiré pattern of the phosphorus atoms in the uppermost layer of the substrate and the average trajectory height of the probe during the sliding process; the contact distance is divided into a strong contact area and a weak contact area according to different heights, and it is determined that the atoms in the strong contact area have a greater influence on friction.

4. The method for regulating interlayer friction of black phosphorus using strain-induced moiré according to claim 1, characterized in that: The simulation and data processing performed in step (2) also includes: analyzing the fast Fourier spectrum under different relative adhesion factors and strains, finding the energy dissipation channels caused by three washboard frequencies: moiré washboard frequency, strain washboard frequency, and traditional stick-slip washboard frequency, as well as schematic diagrams of the three washboard frequencies.

5. The method for regulating interlayer friction of black phosphorus using strain-induced moiré according to claim 1, wherein: The simulation and data processing in step (2) also include: using 16 atoms in the selected area to calculate the number of phonons of the black phosphorus / black phosphorus interface probe and the substrate, and verifying the influence of three washboard frequencies, namely moiré washboard frequency, strain washboard frequency and traditional stick-slip washboard frequency, on friction by analyzing the number of phonons; and calculating the ratio of the energy dissipation excited at each washboard frequency to the total energy dissipation to explore the contribution degree.

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