Method for regulating and controlling friction through strain-induced moire superlattice

Abstract

The invention relates to a strain-induced moire superlattice friction regulation and control method. The method comprises the following steps: (1) establishing a molecular dynamics model consisting of a substrate and a molybdenum disulfide probe arranged on the substrate; (2) executing molecular dynamics simulation and data processing: (1) applying strain to the bottom layer of the substrate to enable the probe to be in common contact with the top layer of the substrate; applying biaxial tensile strain to the model by changing lattice constants of the underlying substrate in x and y directions; and (2) under the condition that the probe and the substrate are in common contact, operating the model, and calculating the friction force between the probe and the substrate under different strains, temperatures, interaction between substrate layers and normal loads in the friction process so as to analyze the change of the moire superlattice morphology and different contributions to the friction force under different working conditions. The invention provides an effective research method for determining the influence of the moire patterns on the friction force in the common contact state and the internal mechanism, and further provides a thought for actively regulating and controlling the friction by regulating and controlling the moire patterns.

Description

Technical Field

[0001] The present invention relates to the technical field of molecular dynamics, and particularly to a method for regulating friction by strain-induced moiré superlattice. Background Art

[0002] Friction is a complex and wonderful physical phenomenon that is ubiquitous in mechanical systems. With the development of emerging technologies such as atomic force microscopy (AFM) and molecular dynamics simulation (MD), many novel friction characteristics have been discovered, including nanoscale friction resonance and structural superlubrication. There is an increasing recognition that in engineering technology, there is an urgent need to understand how physical properties affect friction and achieve "active" control of friction. In previous studies, scholars found that nanoscale friction is affected by factors such as commensurability, normal load, temperature, and sliding speed. In addition, two-dimensional (2D) materials such as graphene and MoS 2 etc. allow large local strains to be induced by stretching or folding the material due to their thin atomic layers and extremely high out-of-plane flexibility. These conditions create opportunities for effective friction control through strain engineering.

[0003] Numerous studies have shown that strain can regulate the frictional force between two-dimensional materials by adjusting the contact state at the interface. Yang et al. found that the friction coefficient of strained multilayer graphene decreases as the tensile strain decreases due to the change in the atomic-scale contact area. Similarly, Wu et al. studied and found that the interlayer frictional force of molybdenum disulfide decreases sharply under the action of tensile or compressive strain. Zhang et al. studied that in-plane strain can reversely regulate the surface friction of suspended graphene by changing the flexibility of graphene, thereby changing the atomic-scale contact quality. With the progress of research, Xu et al. deposited graphene on a stretchable substrate and studied its friction characteristics. Considering the change in the interface contact state, the authors proposed that different strain-related frictions are caused by the transition between two friction mechanisms (contact-quality dominated and wrinkle-dominated). At the same time, these studies inevitably introduced lattice mismatch between atoms.

[0004] Moiré superlattices caused by lattice mismatch often appear in the van der Waals stacking of two-dimensional materials. The assembly of moiré stacking structures has been proven to be an effective method for significantly adjusting the properties of two-dimensional materials. Periodic moiré superlattices can give rise to new properties such as superconductivity, topological conduction channels, and moiré phonons. In addition, moiré superlattices also exhibit excellent capabilities in regulating friction properties. Wang et al. achieved ultra-low friction between graphene interfaces through strain engineering because they found that the positive and negative stresses inside the strain-induced moiré patterns cancel each other out. Bai et al. quantitatively studied the geometric properties of moiré using the mismatch interval statistics method and adjusted the superlubricity of the interface. Recently, Wang et al. reported macroscopic superlubricity on the surface of numerous nanoscale graphene moiré structure assemblies through face hydrogen modulation, which is of great significance for the engineering applications of moiré patterns. In addition, stacking heterojunctions between substrate layers can also construct moiré and regulate friction. For example, Liu et al. found that the frictional stick-slip phenomenon in the graphene / platinum heterostructure occurs simultaneously at the atomic scale and the moiré scale. A similar friction modulation was observed at the graphene / ruthenium interface. It was found that these long-range modulations strongly depend on the tip and moiré, as well as the interlayer interactions inside the moiré. Their origin is attributed to the sliding energy barrier caused by the change in the surface morphology of the moiré due to strong interactions, or the accumulation and release of the in-plane elastic strain energy of the moiré caused by tip sliding.

[0005] The above research shows that strain engineering between two-dimensional materials can induce moiré superlattices to regulate friction, but the potential mechanism of moiré controlling friction is still not fully understood. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method for regulating friction by strain-induced moiré superlattices.

[0007] To solve the above problems, a method for regulating friction by strain-induced moiré superlattices according to the present invention includes the following steps:

[0008] ⑴ Establish a molecular dynamics model composed of a substrate and a molybdenum disulfide probe disposed on the substrate;

[0009] The substrate is bilayer molybdenum disulfide with biaxial tensile strain applied to the bottom layer; the atoms on both sides of the fixed boundary of the upper-layer molybdenum disulfide in the substrate are set as temperature adjustment regions using the Berendsen thermostat method;

[0010] Each atom of the probe is provided with springs in the x, y, and z directions; among them: the spring in the x direction is connected to a virtual slider moving at a constant speed in a fixed direction; the spring in the y direction is used to prevent the probe from rotating around the z axis and translating along the y axis during sliding, and the spring in the z direction is used to apply a normal load;

[0011] ⑵ Perform molecular dynamics simulation and data processing:

[0012] ① Apply strain to the bottom layer of the substrate to make the probe and the top layer of the substrate in commensurate contact. At this time, the lattice mismatch between the two layers of the substrate caused by the strain will lead to the formation of a moiré superlattice on the substrate surface; apply biaxial tensile strain to the model by changing the lattice constants of the bottom substrate in the x and y directions, and set the strained layer as a rigid body to maintain the stability of the moiré shape; the strain change range is from 0% to 20%.

[0013] ② When the probe and the substrate are in commensurate contact, give the slider a speed of 10 m / s, run the model, and calculate the frictional force between the probe and the substrate under different strains, temperatures, interlayer interactions between the substrate layers, and normal loads during the friction process, so as to analyze the changes in the moiré superlattice morphology and its different contributions to the frictional force under different working conditions.

[0014] Performing molecular dynamics simulation and processing data in step ⑵ also includes: performing a fast Fourier transform (FFT) on the interlayer frictional force of molybdenum disulfide under different strains to separate the frequency distribution and amplitude corresponding to the moiré pattern.

[0015] Performing molecular dynamics simulation and processing data in step ⑵ also includes: selecting 24 atoms at the center of mass of the probe to calculate the density of states; analyzing the change mode of the moiré frequency corresponding to different strains from the perspective of the density of states to reveal the phonon mechanism of the change in frictional force under different strains.

[0016] Performing molecular dynamics simulation and processing data in step ⑵ also includes: analyzing the contact state of the moiré pattern exhibited by the probe and the substrate under different strains to determine the influence of surface roughness on friction.

[0017] Performing molecular dynamics simulation and processing data in step ⑵ also includes: for different strains, different interlayer interactions, and different loads, the height of the potential barrier suffered by the model during the friction process is used to determine the different contributions of the moiré phonon frequency and surface roughness to friction.

[0018] Performing molecular dynamics simulation and processing data in step ⑵ also includes: calculating the number of excited phonons at different interfaces of different strains, different interlayer interactions between the substrate layers, and different loads, and intuitively explaining the differences in frictional force under different contact states with the different distributions of the number of phonons.

[0019] The present invention has the following advantages compared with the prior art:

[0020] 1. The present invention takes bilayer molybdenum disulfide as the research object, first establishes a molecular dynamics model, and then runs the model under different strains, temperatures, interlayer interactions of the substrate layer, and normal loads respectively, calculates data such as interlayer frictional force and phonon spectrum during the friction process, and conducts analysis and processing, thereby providing an effective research method for determining the influence of moiré patterns on frictional force and its internal mechanism in the commensurate contact state, and further providing ideas for actively regulating friction by controlling moiré patterns.

[0021] 2. The present invention uses fast Fourier transform to analyze the instantaneous frictional force, combines with the phonon density of states at the friction interface, and finally establishes a new phonon dissipation channel related to moiré patterns, thereby explaining the reason for the significant increase in friction.

[0022] 3. The present invention obtains a calculation method for the surface roughness of moiré patterns by using the difference in the contact state between the probe and different moiré patterns, and further explains the local peak of friction during the strain application process.

[0023] 4. The present invention explains the influence of interlayer interaction of the substrate layer and probe-substrate interaction on moiré pattern modulated friction during the moiré pattern regulating friction process by changing the potential well parameters between the substrate layers during the strain application process and the normal load applied to the probe, expanding the applicable range of this regulation method.

[0024] 5. By using the method of the present invention, it is possible to provide a theoretical reference for realizing the active regulation of interlayer friction of two-dimensional materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The following further elaborates on the specific embodiments of the present invention with reference to the accompanying drawings.

[0026] Figure 1 This is the molecular dynamics model provided by the embodiment of the present invention.

[0027] Figure 2Snapshots of the interlayer friction of molybdenum disulfide and the substrate moiré pattern under different strains provided by the embodiments of the present invention. Among them: (a) is the relationship between the instantaneous friction and the sliding distance when the strain is 0.025; (b) is the relationship between the instantaneous friction and the sliding distance when the strain is 0.05; (c) is the instantaneous friction at a strain level of 0.025 within a single long-range period; (d) is the instantaneous friction at a strain level of 0.05 within a single long-range period; (e) is the contour map of the substrate at a strain level of 0.025; (f) is the contour map of the substrate at a strain level of 0.05; (g) is the relationship between the instantaneous friction and the sliding distance when the strain is 0.07; (h) is the relationship between the instantaneous friction and the sliding distance when the strain is 0.1; (i) is the instantaneous friction at a strain level of 0.07 within a single long-range period; (j) is the instantaneous friction at a strain level of 0.1 within a single long-range period; (k) is the contour map of the substrate at a strain level of 0.07; (l) is the contour map of the substrate at a strain level of 0.1.

[0028] Figure 3 The average friction forces under different strains, different interlayer interactions of the substrate, and different temperatures provided by the embodiments of the present invention.

[0029] Figure 4 The fast Fourier transform of the instantaneous friction force under different strains provided by the embodiments of the present invention. Among them: (a)-(d) are the FFT spectra when the strains are 0.025, 0.05, 0.07, and 0.1 respectively. f w and f m respectively represent the washboard frequency and the moiré washboard frequency.

[0030] Figure 5 The interfacial phonon spectra under different strains provided by the embodiments of the present invention. Among them: (a)-(c) are the density of states (DOS) of the probe when the strains are 0.05, 0.08, and 0.1 respectively; (d) is the moiré washboard frequency (blue) and the moiré pattern period length (red) calculated according to Equation (1) as a function of strain.

[0031] Figure 6 The change in the amplitude of the moiré washboard frequency in the fast Fourier transform and the change in the probe amplitude and surface roughness under different strains provided by the embodiments of the present invention. Among them: (a) is the dependence of the amplitude of the moiré washboard frequency in the FFT spectrum on different strain levels; (b) is the peak-to-valley value and the corresponding height difference of the z coordinate of the moiré pattern in the substrate under different strain levels; (c) is the relationship between the amplitude of the centroid trajectory of the probe and the surface roughness and the strain level. The pink dashed line represents Figure 3 the surface roughness when the friction force recovers and rises in

[0032] Figure 7Variation of the interfacial barrier under different strains provided by the embodiments of the present invention. Wherein: (a)-(e) are the total energy barrier and the molar barrier when the strain is 0.025, 0.05, 0.07, 0.1, and 0.2, respectively; (f) is the stick-slip energy barrier at different strain levels.

[0033] Figure 8 Variation of the interfacial barrier under the same strain and different interactions between the substrate layers provided by the embodiments of the present invention. Wherein: (a)-(b) are the total energy barrier and the molar barrier when λ = 2.5 and λ = 10 and the strain is 0.05, respectively; (c) is the stick-slip energy barrier at different λ values; (d) is the correlation and amplitude of the FFT at the molar corrugation frequency at different λ values; (e) is the peak-to-valley value of the z coordinate of the moiré pattern at different λ values, and the insets are snapshots of the substrate moiré pattern at λ = 2.5 and λ = 10, respectively.

[0034] Figure 9 Variation of the interfacial barrier under the same strain and different normal loads provided by the embodiments of the present invention. Wherein: (a) is the variation of the average frictional force under different normal loads; (b)-(c) are the variations of the total energy barrier and the molar stick-slip energy barrier under the normal loads of 0.02 nN and 0.1 nN, respectively; (d) is the variation of the stick-slip energy barrier under the normal loads of 0.02 nN and 0.1 nN; (e) is the peak-to-valley value of the z coordinate of the moiré pattern under different normal loads, and the insets show snapshots of the substrate moiré pattern under the normal loads of 0.02 nN and 0.1 nN, respectively, and the correlation between the amplitudes of the molar corrugation frequencies in the FFT under different normal loads.

[0035] Figure 10 Frequency distribution of the number of phonons under different strains, different interactions between the substrate layers, and different normal loads provided by the embodiments of the present invention. Wherein: (a) is the dependence of the excited phonons on the strain, fn = 0.01 nN; (b) is an enlarged image of (a); (c) is the dependence of the excited phonons on λ; (d) is an enlarged image of (c); (e) is the dependence of the excited phonons on the normal load; (f) is an enlarged image of (e). Detailed implementation manners

[0036] A method for regulating friction by strain-induced moiré superlattice, comprising the following steps:

[0037] ⑴ Establish a molecular dynamics model consisting of a substrate and a molybdenum disulfide probe disposed on the substrate;

[0038] The substrate is a bilayer molybdenum disulfide with biaxial tensile strain applied to the bottom layer; the atoms on both sides of the fixed boundary of the upper-layer molybdenum disulfide in the substrate are set as temperature adjustment regions by the Berendsen thermostat method.

[0039] Each atom of the probe is provided with springs in the x, y, and z directions; among them: the spring in the x direction is connected to a virtual slider moving at a constant speed in a specific direction; the spring in the y direction is used to prevent the probe from rotating around the z axis and translating along the y axis during sliding, and the spring in the z direction is used to apply a normal load.

[0040] ⑵ Perform molecular dynamics simulation and data processing:

[0041] ① Apply strain to the bottom layer of the substrate to make the top layer of the probe and the substrate commensurate in contact. At this time, the lattice mismatch between the two layers of the substrate caused by the strain will lead to the formation of a moiré superlattice on the substrate surface; apply biaxial tensile strain to the model by changing the lattice constants of the bottom substrate in the x and y directions, and set the strained layer as a rigid body to maintain the stability of the moiré shape; the strain change range is from 0% to 20%.

[0042] ② In the case where the probe and the substrate are in commensurate contact, give the slider a speed of 10 m / s, run the model, and calculate the frictional force between the probe and the substrate under different strains, temperatures, interlayer interactions between the substrate layers, and normal loads during the friction process, and then use it to analyze the changes in the moiré superlattice morphology and its different contributions to the frictional force under different working conditions.

[0043] In the present invention, performing the simulation process and processing data also includes:

[0044] Perform a fast Fourier transform (FFT) on the interlayer frictional force of molybdenum disulfide under different strains to separate the frequency distribution and amplitude corresponding to the moiré pattern.

[0045] Select 24 atoms at the center of mass of the probe to calculate the density of states; analyze the change mode of the moiré frequency corresponding to different strains from the perspective of the density of states to reveal the phonon mechanism of the change in frictional force under different strains.

[0046] Analyze the contact state of the moiré pattern shown by the probe and the substrate under different strains to determine the influence of surface roughness on friction.

[0047] For different strains, different interlayer interactions, and different loads, determine the height of the potential barrier suffered by the model during the friction process to determine the different contributions of the moiré phonon frequency and surface roughness to friction.

[0048] Calculate the number of excited phonons at the interfaces with different strains, different interlayer interactions, and different loads, and intuitively explain the differences in frictional force under different contact states with the different distributions of the number of phonons.

[0049] Embodiment

[0050] The present invention takes molybdenum disulfide as the research object, explores the change of friction with strain under different substrate interlayer interactions and normal loads by constructing moiré patterns on the substrate surface, and studies the phonon mechanism of its frictional energy dissipation. The specific process is as follows:

[0051] (1) Establish a molecular dynamics model

[0052] The present invention uses the molecular dynamics simulation method based on LAMMPS to realize the simulation process.

[0053] Figure 1 is a schematic diagram of the established molecular dynamics model. In the present invention, the molecular dynamics model includes a probe of a square molybdenum disulfide thin sheet (6048 atoms) sliding on a fixed-supported single-layer molybdenum disulfide substrate (26208 atoms). The probe size is 13.4×13.2 nm 2 , and the substrate size is 13.4 nm and 28.8 nm in the x and y directions respectively. Therefore, the probe and the substrate have the same size in the x direction.

[0054] To construct the moiré pattern and maintain the molybdenum disulfide configuration, biaxial strain is applied to the underlying fixed support. To simulate the stiffness of the AFM cantilever and ensure the smooth movement of the probe, each probe atom is connected to a spring in the x, y, and z directions. A set of springs with a stiffness of 3000 nN / nm in the x direction is used to connect the center of mass of the probe to a virtual slider with a sliding speed of v s , guiding the probe to slide relative to the substrate. To constrain the translation and rotation in the y direction, springs with a stiffness of 2000 nN / nm are applied. Springs with a stiffness of 1000 nN / nm in the z direction are used to apply the normal load. On both sides of the contact area are Berendsen thermostats and fixed MoS 2 atom boundaries, and the thermostat regulates the temperature of the entire system.

[0055] The microcanonical ensemble with fixed volume, number of particles, and energy is selected to calculate the simulation process.

[0056] The present invention uses two Lennard-Jones (LJ)-type vdW potentials to characterize the atomic interactions between the probe and the substrate (LJ-0) and between different MoS 2 layers of the substrate (LJ-1). The LJ potential is widely used to simulate the friction of molybdenum disulfide materials and has been found to reproduce behavior consistent with experiments.

[0057] In the LJ potential, the interaction potential is expressed as

[0058] U(r) = 4ε[(σ / r) 12 -(σ / r) 6 (1)

[0059] In the formula: ε is the depth of the potential well; σ is the characteristic distance when the potential well is zero; r is the characteristic distance.

[0060] For the interaction between the probe and the substrate, i.e., LJ-0, the present invention uses σ 0 = 3.18 Å t and ε = 0.0236 eV. For the LJ potential between the upper substrate and the fixed support (i.e., LJ-1), the present invention uses σ = σ 0 and ε = λε 0 of the LJ parameters, where λ is the relative adhesion factor, representing the ratio of the adhesion strength between the substrate molybdenum disulfide - molybdenum disulfide and the probe - substrate.

[0061] The Stillinger - Weber (SW) potential is used to characterize the Mo - S covalent bond between atoms within the molybdenum disulfide layer. The phonon density of states (DOS) at the friction interface is calculated from 24 atoms selected from the probe and the substrate.

[0062] The system is relaxed for 0.1 ns, and then a velocity of 10 m / s is applied to the probe in the x - direction to slide it along the zigzag direction of the substrate. The time step is set to 0.5 fs, which is much lower than the fastest phonon annihilation time, allowing extraction of all friction - related information generated by dynamic excitation.

[0063] (2) Determine the influence of moiré patterns on friction during the strain application process and its internal mechanism

[0064] (21) Determine the influence of moiré patterns on the friction of molybdenum disulfide

[0065] Applying in - plane strain changes the lattice constant and atomic overlap between adjacent atoms, thus affecting the interaction between atoms during the sliding process. Based on Figure 1 the friction model established in Figure 2 (a)-(d) and (g)-(j) show that during the probe sliding process, in addition to the well - known stick - slip cycle determined by the lattice constant of the contact interface, a long - distance friction modulation phenomenon with a larger period can also be observed. Since the probe slides along the zigzag direction while the lattice constant of the contact interface remains unchanged, the stick - slip cycle remains constant, where a is the projection length of the Mo - S bond in the x - y plane. However, as the strain increases, the long - range modulation period of the instantaneous friction force shortens.

[0066] At Figure 2(e), (f), (k) and (l), a series of moiré superlattice structures with different periodicities can be formed under various strains, which will affect the contact state between the probe and the substrate. Further measure the distance between two moiré patterns in the sliding direction. At strains of 0.025, 0.05, 0.07 and 0.1, the moiré pattern period lengths are 13.1 nm, 6.7 nm, 4.9 nm and 3.5 nm respectively, which match the long-range periodicity of the frictional force. Therefore, it can be confirmed that the long-distance friction modulation phenomenon is attributed to the moiré topography exhibited by the substrate.

[0067] The moiré size can be calculated by the following formula:

[0068]

[0069] where: a is the projected length of the Mo-S bond in the x-y plane; ε is the magnitude of the interlayer strain between the bottom substrate and the 2 underlying substrate; θ represents the twist angle.

[0070] Observation of the moiré pattern ( Figure 2 (e), (f), (k) and (l)) shows that the moiré pattern is composed of a hexagonal structure, where the higher central region is surrounded by the lower region. At the center of the hexagonal lattice, lattice mismatch causes some atoms of the lower substrate support layer to completely coincide with some atoms of the upper substrate layer, called the AA stacking order, which in turn leads to the highest uplift amplitude. In the transition region from the center to the edge of the moiré pattern, the atoms gradually change from AA stacking to AB stacking, resulting in a gradual decrease in the uplift amplitude. Finally, it completely evolves into the AB stacking mode with higher stability, lower interlayer potential and higher stiffness than the AA stacking order atoms. Therefore, the distance between the centers of two adjacent moiré patterns (defined as the period of each moiré pattern) is actually the distance of the AA stacking mode.

[0071] As Figure 3 shown, the average frictional force increases non-monotonically with the increase of strain. At the same strain, the average frictional force gradually decreases with the increase of the interlayer interaction. At λ = 1 and λ = 2.5, there are friction peaks at strains of 0.025 and 0.05 ( Figure 3 the blue dashed line in); at λ = 10, the peak disappears. In addition, the present invention also considers the influence of temperature on the tribological properties. Compared with 0K, at a temperature of 100K, due to the enhanced atomic thermal vibration, the interlayer frictional resistance decreases, but the non-monotonic upward trend of friction remains unchanged.

[0072] (22) Study the intrinsic mechanism of the strain dependence of moiré-modulated friction

[0073] (221) Separate the contribution of the moiré corrugation frequency to friction by performing a fast Fourier transform on the instantaneous frictional force.

[0074] To understand the relationship between friction and moiré superlattice, the frequency and amplitude distributions of the probe related to the moiré superlattice are separated by performing a fast Fourier transform (FFT) on the instantaneous friction. As can be seen from Figure 4 , the components of friction are located at several discrete frequencies. Further investigation shows that these discrete frequencies are the corrugation frequencies of the probe and their harmonics f = nf t (n = 1, 2, 3...)(marked with red dashed lines). Therefore, the moiré corrugation frequency is defined as f m = v s / R, where R is the moiré size. It is found that a peak also appears at the moiré corrugation frequency, which is in good agreement with the long-distance modulation period of the instantaneous friction. The unique peak in the FFT spectrum indicates that the presence of the moiré superlattice contributes to the friction during the system motion.

[0075] (222) phonon spectrum interprets the moiré phonon dissipation channels and their evolution laws.

[0076] Research shows that the energy at the friction interface mainly exists in the form of phonons, and the transport of these phonons depends on the energy dissipation channels between the contact interfaces. Given this property, it can be speculated that the presence of the moiré superlattice will trigger new energy dissipation channels at the contact interface, thereby improving the phonon transport efficiency and resulting in an increase in friction.

[0077] To test the above hypothesis, the present invention calculates the DOS value that can monitor the contribution of phonons to friction. To obtain the DOS value, FFT is applied to the velocity autocorrelation function (VAF) as follows:

[0078]

[0079] where: ω is the angular frequency; τ is 0.5 ns; <ν(t)ν(0)> represents the VAF; <> represents Figure 1 the time average of all atoms in the selected region shown in; i is the imaginary symbol; t is the time.

[0080] As Figure 5 (a)-(c) shows, a new peak also appears at the moiré corrugation frequency in the DOS spectrum. The appearance of this new peak indicates the formation of new energy dissipation channels. As the strain increases, the two acoustic modes (corresponding to the moiré corrugation frequency and the corrugation frequency) become closer. The degree of matching of the phonon excitation frequencies reflects the coupling strength of the vibration modes at the contact interface. The strong coupling between the acoustic modes improves the energy transfer efficiency, resulting in more effective phonon transfer between atoms at the contact interface, thereby leading to an increase in friction.

[0081] Figure 5 (d) shows the correspondence between the moiré period and the moiré washboard frequency and strain. It is worth noting that each atom on the contact surface is subject to the interaction of the opposite potential, so the dissipation channels shown by the probe DOS actually correspond to the moiré topography of the substrate, which is consistent with the aforementioned assumption.

[0082] (223) Calculate the change of the substrate moiré height and the probe trajectory with strain to find the correct representation of the moiré surface roughness.

[0083] In addition to the distribution of the moiré washboard frequency, the change in amplitude corresponding to these frequencies in the FFT spectrum also indicates the evolution of the frictional energy contribution. As Figure 6 (a) shows, with the change of strain, the amplitude of the moiré washboard frequency first increases and then decreases. Two peaks appear at strains of 0.025 and 0.05, which is very consistent with the positions of the peaks of the average frictional force. Therefore, the non-monotonic change in the amplitude of the moiré washboard frequency in the FFT spectrum may be another factor affecting friction.

[0084] In addition, the moiré period lengths corresponding to the two peaks are 13.1 nm and 6.7 nm, which are close to the size of the probe length (13.4 nm) and its radius (6.7 nm) in the sliding direction. Since the long-range friction modulation is closely related to the moiré topography of the substrate, the moiré surface roughness is an important parameter affecting the long-range friction modulation. Based on this, the present invention calculates the change of the moiré height with the increase of strain. As Figure 7 (b) shows, the size of the moiré pattern decreases with the increase of strain, resulting in fewer atoms with lattice distortion within the moiré period. The peak-to-valley values of the z coordinate converge at almost the same rate, and the moiré height decreases monotonically. The substrate contact surface seems to become gradually flat. However, the trend of the monotonically decreasing height is inconsistent with the non-monotonic change of the FFT amplitude.

[0085] Recent studies have shown that the surface roughness of the moiré can be represented by the center-of-mass (COM) trajectory of the probe. Continue to calculate the fluctuation H 2 of the COM trajectory of the probe as a function of strain. As Figure 6 (c) shows, H 2 exhibits a non-monotonic change similar to the FFT amplitude. This is because, although all cases in this study so far have the same probe size and the same normal load, when corresponding to different moiré period lengths, the contact state between the probe and the substrate may be different, especially when the moiré period length is less than the probe size. Therefore, the change in the height of the substrate moiré cannot fully reflect the surface roughness.

[0086] As Figure 6 (c) and (d) show, the roughness R c = H2 / R (height change of the COM trajectory of the probe within one moiré period) is consistent with the FFT change. This is because when the moiré size R > L (L is the size of the probe in the sliding direction), the probe can be in full contact with the moiré surface. Therefore, the probe is forced to experience large normal fluctuations to adapt to the moiré pattern, and at this time, the substrate moiré height can determine the COM trajectory of the probe. When L / 2 < R < L, the probe will contact multiple moiré patterns, resulting in unstable trajectory fluctuations. R c Non-monotonic changes may even occur.

[0087] When R ≤ L / 2, the hump-shaped regions of the contact pattern (with closer contact distances) can be regarded as the struts supporting the sliding of the probe. Therefore, the COM fluctuations of the probe decrease, and R c also decreases. R c The maximum value of R appears at L / 2 = 6.7 nm. In this case, no matter how the probe moves, the probe is always completely lifted by two sets of moiré humps. With further increase of the strain, although the moiré distribution in the contact area becomes denser, due to the gradual decrease of the hump height, the COM fluctuations of the probe decrease. Therefore, the amplitude of the moiré washboard frequency in the FFT is determined by the FFT, and this amplitude is calculated based on the fluctuations R c of the probe COM, rather than based on the height of the substrate moiré pattern.

[0088] (224) The difference in friction force under different strains is explained by the barrier height.

[0089] The magnitude of friction can be attributed to the difficulty of crossing the obstacle, and the energy barrier height can be obtained by the difference between the maximum and minimum van der Waals potentials between the layers.

[0090] To verify the above theory, the energy barriers under different strains were measured. As Figure 7 (a)-(e) show, the change of the total barrier height is in good agreement with the change of the average friction force. In addition, the moiré long-range periodic phenomenon also appears in the images of some energy barriers. An attempt was made to separate the moiré stick-slip energy barrier (MSEB) from the stick-slip energy barrier (SEB). First, the change of the MSEB height is almost consistent with the change of the amplitude at the moiré washboard frequency in the FFT spectrum, and the peak of the MSEB height appears at the peak of the surface roughness. A rougher contact surface will increase the energy barrier, which means greater resistance needs to be overcome, thus increasing the friction. Continuing to observe the SEB, the stick-slip cycle corresponding to the atomic scale occurs in all cases. Since the direction of the hexagonal lattice is the same as the probe sliding direction, it has almost the same periodicity. Observe the change of the SEB height, as Figure 7(f). Compared with a strain of 0.025, SEB has a significant height difference at a strain of 0.05. This is because, except for a brief decrease after the peak at a strain of 0.025, both the phonon coupling strength and the surface roughness increase before a strain of 0.05. These two factors synergistically promote the rapid rise of SEB. After the strain exceeds 0.05, the surface roughness begins to decrease while the phonon coupling strength continues to increase. The smoother substrate surface reduces the sliding resistance, which also affects SEB. At strains of 0.07 and 0.1, the competition between the two slightly reduces SEB. Due to the rapid decrease in surface roughness, the influence of phonon frequency on the total energy barrier gradually dominates after a strain of 0.11 ( Figure 5 the green dashed line in). Therefore, SEB continues to rise after a period of decline, corresponding to Figure 5 the friction recovery in. Observe Figure 9 the energy barrier at a strain of 0.2 in (e). The influence of MSEB on friction is very small, and the friction is almost entirely contributed by SEB.

[0091] From the above analysis, it can be concluded that the influence of surface roughness on frictional resistance is manifested as a change in the height of MSEB. The phonon frequency regulates the frictional force by affecting SEB, but SEB is also affected by surface roughness.

[0092] (225) Calculate the influence of the change in the interlayer interaction of the substrate layer on the moiré topography, interface barrier, and surface roughness using the relative adhesion factor.

[0093] As revealed by the aforementioned simulations, the change in frictional force depends on the evolution of the moiré pattern, and the moiré pattern is caused by the interlayer interaction of the substrate layer. Next, the influence of the interlayer interaction on moiré friction modulation is explored. As Figure 3 shown, the average frictional force decreases with the increase in interlayer interaction. The friction reaches a peak at strains of 0.025 and 0.05, weakens when increasing from 1-fold to 2.5-fold, and completely disappears when reaching 10-fold. In addition, regardless of λ, the frictional force will eventually tend to the same value.

[0094] To explore the reason, the energy barriers at the same strain under different conditions were measured. Figure 8 (a)-(c) illustrate the changes in MSEB and SEB when λ increases to 2.5-fold and 10-fold at a strain of 0.05. Generally speaking, the barrier height decreases with the increase in λ, indicating that the stronger the interaction between the two substrate layers, the lower the energy barrier. Compared with the energy barrier in Figure 7 (b), with the increase in interlayer interaction, both the height of SEB and the height of MSEB decrease. The periodic MSEB even almost disappears at λ = 10. Based on the above analysis, both MSEB and SEB are affected to varying degrees by the moiré superlattice hump structure. According toFigure 8 (c), when λ = 2.5, before a strain of 0.2, its variation is similar to that when λ = 1, but the amplitude is significantly lower. When the strain reaches 0.2, due to the shortening of the moiré period length, the number of atoms experiencing lattice distortion in one moiré period decreases. Due to the limitation of the number of atoms in the lattice distortion, the variations of the surface roughness at different λ gradually tend to be consistent, which leads to the ultimate consistency of the average friction at different λ.

[0095] Further measure R at the same strain c and the variation of the moiré pattern. At the same strain, the spacing of the moiré humps is fixed. Figure 8 (d) and (e) show the variations of the peak-to-valley values in the z direction, the evolution of the moiré pattern, and the peak-to-valley values of the corresponding FFT amplitude at the moiré corrugation frequency. When the interlayer interaction increases, the center of the moiré pattern in the energetically unfavorable stacking region of the AA stacking is destroyed. Some of the aligned atoms approach each other and become misaligned under strong interaction, forming a transition region between the AA stacking and the AB stacking. The transition region also transforms into the AB stacking, resulting in a decrease in the hump height. In the energetically favorable stacking region, the AB stacking region with a lower interlayer potential is less affected by λ and remains relatively stable. The strong interlayer interaction finally fixes the upper-layer MoS 2 tightly on the support. This weakens the two types of energy barriers and sliding instability, thus suppressing the moiré modulation. The probe atoms can more easily pass through the barriers, reducing the energy consumed during the oscillation process and decreasing the amplitude of the moiré corrugation frequency in the FFT spectrum. When λ = 10, the contribution of the friction caused by the MSEB almost disappears. Therefore, within the entire strain range, the friction is almost completely affected by the phonon frequency, resulting in an almost monotonic increase in the average friction force.

[0096] (226) Reveal the influence of the change in the interaction between the probe and the substrate on the moiré friction by changing the normal load.

[0097] The present invention further considers the quantitative relationship among the moiré period, the load, and the friction. Under the compressive normal load, the probe may similarly affect the MoS 2 lattice, and then regulate the potential of the interaction between the probe and the substrate. As Figure 9 (a) shows, the average friction force increases with the increase of the normal load, and more energy is dissipated, which is consistent with the traditional friction law. The magnitude of the average friction force under the same load is consistent with its variation pattern at different strains, indicating that the modulation of the moiré period on the friction force is stable under different loads. Figure 9(b)-(d) show the potential barriers under different loads. When the strain is 0.2 and the load is 0.02 nN, the change caused by the strain corresponding to MSEB is very small, enabling the subtle changes in the two energy barriers to be clearly observed. When the load increases to 0.1 nN, both types of energy barriers increase simultaneously.

[0098] Continue to observe the evolution of the moiré topography and FFT amplitude, as Figure 9 shown in (e). The inset shows the changes in the moiré pattern at loads of 0.02 nN and 0.1 nN. As the load increases, the lattice bends and deforms in the substrate contact area. However, at large loads, the moiré pattern can still effectively resist the compression of the probe, which is consistent with the results of Song et al.

[0099] Under the action of the load, the nesting degree between the probe and the substrate increases, resulting in an increase in SEB. The change in the peak-to-valley value of the z coordinate indicates that the atomic positions in the AA and AB stacking regions decrease simultaneously. However, under the weak van der Waals interaction of λ = 1, the atomic stacking pattern remains relatively stable. As the load increases, some atoms in the AB stacking show relatively greater flexibility under pressure due to the gaps between them. As a result, the atoms in the AB stacking descend faster than those in the AA stacking, leading to a gradual increase in the difference between the peak-to-valley values of the z coordinate. An increase in λ causes an increase in MSEB, resulting in a higher FFT amplitude at the moiré corrugation frequency. The dependence and FFT amplitude corresponding to the moiré corrugation frequency under different loads can be as Figure 9 shown in the inset of (e).

[0100] (227) Quantitatively reveals the change in frictional energy dissipation by calculating the number of phonons excited at the contact interface under different working conditions.

[0101] Due to phonon coupling and the associated finite phonon lifetime, the energy obtained by a specific phonon mode from these instabilities is considered to be rapidly redistributed over the entire possible phonon full spectrum. To quantify the frictional energy dissipation at the moiré superlattice, the number of phonons excited by atoms at the frictional interface was further calculated, as Figure 10 shown.

[0102] The number of excited phonons at frequency ω is calculated as follows:

[0103]

[0104] where: N represents the number of atoms per unit volume, m represents the atomic mass, h represents the reduced Planck constant, ω represents the angular frequency, and S V (ω) represents the power spectral density.

[0105] As Figure 10As shown in (a), (c), and (e), the total amount of non-equilibrium phonons excited at the contact interface is in good agreement with the changes in friction force under different strains, λ, and loads. They are mainly distributed at the corrugation frequency, its harmonics, and the Moiré corrugation frequency. The energy dissipation channels formed at the corresponding positions enable the vibrational kinetic energy to be effectively transferred from the probe to the substrate, thereby causing changes in energy dissipation.

[0106] Due to the significant differences in the internal states between Moiré patterns under different working conditions, Moiré phonons exhibit different evolution patterns. As Figure 10 shown in (b), the changes in the number of Moiré phonons under different strains are consistent with the evolution law of the effective energy dissipation channels. In addition, the coupling strength of the two types of phonon modes is mapped by the positions of the excited phonons that gradually approach. Under different λ and loads, as Figure 10 shown in (d) and (f), the number of Moiré phonons is also affected by the evolution of the Moiré pattern morphology caused by atomic reconstruction, manifested as a decrease in the number of Moiré phonons and a decrease in the friction phonon dissipation with the increase of λ. With the increase of the load, the number of Moiré phonons increases and the phonon dissipation increases.

[0107] In summary, the present invention creates a Moiré superlattice between two basal layers of molybdenum disulfide by adjusting the biaxial strain on the bottom layer of the substrate and reveals the dependence of friction on these Moiré patterns. It is found that with the increase of the applied strain, the friction force shows non-monotonic enhancement. At the same time, the present invention shows that the harmonic coupling of interface phonons improves the energy transfer efficiency, and the non-monotonic change in surface roughness caused by the Moiré pattern also modulates the friction. Moreover, the relationship between phonon coupling and surface roughness develops in a way that is sometimes cooperative and sometimes competitive, jointly leading to the non-monotonic enhancement of friction. In addition, by appropriately introducing the relative adhesion factor and changing the normal load, the present invention studies the influence of the interaction between basal layers and the interaction between the tip and the substrate on Moiré friction.

[0108] Therefore, the present invention provides an atomic insight into the active regulation of friction by quantitatively controlling strain and Moiré pattern, which can further guide the application of strain-stacked materials in multifunctional devices.

[0109] The description of the above embodiments is only used to help understand the method and its core idea of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and modifications can be made to the present invention, and these improvements and modifications also fall within the protection scope of the claims of the present invention.

Claims

1. A method for controlling friction of a strain-induced moiré superlattice, comprising the following steps: (1) Establishing a molecular dynamics model consisting of a substrate and a MoS2 probe disposed on the substrate; The substrate is a double-layer molybdenum disulfide with a biaxial tensile strain applied to the bottom layer; the atoms on both sides of the fixed boundary of the upper layer of molybdenum disulfide in the substrate are set as temperature adjustment areas by using the Branderson temperature adjustment method; Each atom of the probe is x , y , z Springs are provided in three directions; among them: x The spring in the direction is connected to a virtual slider that moves at a constant speed in a certain direction; 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 is used to apply the normal load; ⑵Perform molecular dynamics simulation and data processing: ① Strain is applied to the bottom layer of the substrate, so that the probe and the top layer of the substrate are in contact with each other. At this time, the lattice mismatch between the two layers of the substrate caused by the strain will lead to the formation of a moiré superlattice on the surface of the substrate; x and y The lattice constant of the underlying substrate is changed in the direction to apply biaxial tensile strain to the model, and the strain layer is set as a rigid body to maintain the stability of the moiré shape; the strain variation range is 0% to 20%; ② When the probe and the substrate are in full contact, give the slider a speed of 10 m / s, run the model, and calculate the friction force between the probe and the substrate under different strains, temperatures, substrate layer interactions and normal loads during the friction process, which is then used to analyze the changes in the moiré superlattice morphology under different working conditions and their different contributions to the friction force.

2. The method for controlling friction using a strain-induced moiré superlattice according to claim 1, characterized in that: The execution of molecular dynamics simulation and data processing in step (2) also includes: performing fast Fourier transform on the friction between molybdenum disulfide layers under different strains to separate the frequency distribution and amplitude size corresponding to the moiré pattern.

3. The method for controlling friction using a strain-induced moiré superlattice according to claim 1, characterized in that: Executing molecular dynamics simulation and processing data in step (2) also includes: selecting 24 atoms at the center of mass of the probe to calculate the state density; analyzing the change of the moiré frequency corresponding to different strains from the perspective of state density, revealing the phonon mechanism of the change of friction force under different strains.

4. The method for controlling friction using a strain-induced moiré superlattice according to claim 1, wherein: The performing of molecular dynamics simulation and data processing in step (2) also includes: analyzing the contact state of the moiré patterns exhibited by the probe and the substrate under different strains to determine the influence of surface roughness on friction.

5. The method for controlling friction using a strain-induced moiré superlattice according to claim 1, characterized in that: The molecular dynamics simulation and data processing in step (2) also include: the potential barrier height to which the model is subjected during the friction process under different strains, different interlayer interactions and different loads is used to determine the different contributions of the moiré phonon frequency and surface roughness to friction.

6. The method for controlling friction using a strain-induced moiré superlattice according to claim 1, characterized in that: The execution of molecular dynamics simulation and data processing in step (2) also includes: calculating the number of excited phonons at different strains, interactions between different substrate layers and different load interfaces, and using the difference in the distribution of the number of phonons to intuitively explain the difference in friction force under different contact states.

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