CN109444475A - The research method that frictional force is contributed in a kind of probe thin slice and each contact zone of substrate - Google Patents

The research method that frictional force is contributed in a kind of probe thin slice and each contact zone of substrate Download PDF

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CN109444475A
CN109444475A CN201811408414.2A CN201811408414A CN109444475A CN 109444475 A CN109444475 A CN 109444475A CN 201811408414 A CN201811408414 A CN 201811408414A CN 109444475 A CN109444475 A CN 109444475A
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rigidity
frictional force
gradient
substrate
atom
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董赟
冯瑞成
朱宗孝
陈卫华
何天经
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Lanzhou University of Technology
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Lanzhou University of Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01Q—SCANNING-PROBE TECHNIQUES OR APPARATUS; APPLICATIONS OF SCANNING-PROBE TECHNIQUES, e.g. SCANNING PROBE MICROSCOPY [SPM]
    • G01Q60/00—Particular types of SPM [Scanning Probe Microscopy] or microscopes; Essential components thereof
    • G01Q60/24—AFM [Atomic Force Microscopy] or apparatus therefor, e.g. AFM probes
    • G01Q60/26—Friction force microscopy

Abstract

The invention discloses the research methods that frictional force is contributed in a kind of probe thin slice and each contact zone of substrate, comprising the following steps: step 1 establishes Frictional model between the graphene layer that rigidity gradient supports under commensurability contacts using Molecular Dynamics method；Step 2 analyzes the contribution of substrate and each contact zone of thin slice to friction energy loss under different base mass center rigidity and support stiffness gradient.Driving force is contributed in soft-sided battery limit (BL) always, and the frictional force of hard-edge battery limit (BL) contribution is maximum, and with the increase of support stiffness, hard-edge battery limit (BL) is higher than also to the contribution always to rub；Step 3 illustrates rigidity gradient to the inherent mechanism of each contact zone friction effects.The frictional force of each contact zone is the result that the interface fold gesture between thin slice and substrate and the normal deformation difference between contact zone are coupled.

Description

The research method that frictional force is contributed in a kind of probe thin slice and each contact zone of substrate
Technical field
The invention belongs to molecular dynamics technical field, it is related to a kind of probe thin slice and each contact zone of substrate to frictional force tribute The research method offered.
Background technique
When the object that two contact occurs relative motion or has relative motion trend, the power of its relative motion is hindered to claim For frictional force, this phenomenon or characteristic between contact surface are friction.Friction is substantially under contact surface atomic interaction Irreversible energy dissipation, be related to complicated nonequilibrium thermodynamics process.It is analyzed from the atomic scale of component, it is smooth to connect Touching becomes numerous rough peak contacts, and the continuous media contact theory of macroscopic view application is no longer desirable for microcosmic discrete touch model. Graphene is a kind of two-dimentional carbon material with atomic-level thickness, because of its distinctive bigger serface structure, it is considered to be ideal Frictional force research material.Simultaneously as it is with the properties such as excellent mechanics, calorifics, electrical and optical, it is believed that it will It is possible that replacing silicon, the new carbon epoch are opened.The application study of current graphene-based device rapidly develops, nano-transistor, Transparent conductive film, high sensor, micro-/nano electromechanical systems etc. all achieve substantive progress.It is received some In rice device, relative motion between graphene layer induces mechanical work, simultaneously because the weaker Van der Waals force of its interlayer and stronger Covalent bond effect in layer, multi-layer graphene can be used as ideal solid lubricant.Then, using graphene as research object, from The length dimension of atom level and the time scale of phonon grade observe friction phenomenon, probe into its rule, clear Related Mechanism, construct and receive Rice frictional theory has become current Nanotribology research contents of greatest concern.
Based on the importance of scale driving and energy conversion is received, people cause extensively the research of nano-device directed movement General concern.The carbon nanotube both ends outside achirality such as Bailey apply DC voltage and generate electric current, make carbon nanotube shape in chirality At rotation torque to overcome the frictional force between inner and outer pipes to make rotating motion.Guo etc. is by experiment in a double-walled carbon nano-tube Pipe both ends find that shorter outer tube can do orientation translation or rotation, even if changing impressed current direction, outer tube after applying electric current Motion state will not change, this phenomenon is attributed to the heterogeneity that initial current generates inner tube in axial direction by author The temperature gradient that hot-fluid is formed, causes the Van der Waals potential energy difference and fillet transition position thermal vibration amplitude of inner and outer pipes contact zone The collective effect of difference drives outer tube to move.Somada etc. has found a capsule-type carbon nanotube in length using transmission electron microscope Linear reciprocating motion is done in nanotube, and demonstrates driving force with molecular dynamics and is caused by two parts, is outer tube end respectively The system capacity that model ylid bloom action between wall cap and capsule absorbs causes outer tube both ends formation energy paddy and thermal vibration to lead The nanotube axial direction tucking of cause.Shiomi etc. and Coluci etc. is also respectively by water cluster and fullerene in carbon nanotube In directed movement confirm that driving force is caused by temperature gradient.It is different from the past to be continuously applied in carbon pipe or substrate both ends Sawtooth pattern (zigzag) graphene platelet is placed on rigidity gradient and supported by driving force of the external excitation to keep constant, Chang etc. The graphene-based bottom armchair (armchair) on (non-commensurability contact), discovery thin slice can spontaneously from rigidity smaller area to Large area sliding, illustrates that the difference of internal system own material attribute can induce the driving force in rigidity gradient direction.Work as device When slipping over two different bound base bottoms or two kinds of material interfaces, since the difference of elasticity modulus of materials causes supporter in sliding side It is upwardly formed rigidity gradient, and Van der Waals potential energy when commensurability contact between interface is small, contact is stablized, and the secondary interfaces of two frictions lead to Often contacted in a manner of commensurability.So being hindered in conjunction with caused by the driving force and the lower interface fold gesture of commensurability contact of rigidity gradient induction Hinder the sliding behavior of power research nano-device extremely important.And commensurability contact and substrate support rigidity gradient between graphene layer are become Change the relative motion combined, domestic and foreign scholars rarely have research.Therefore, the variation of research substrate support rigidity gradient is to frictional force shadow It rings, there is important science and realistic meaning.
Summary of the invention
The purpose of the present invention is to provide the research methods that frictional force is contributed in a kind of probe thin slice and each contact zone of substrate.
Itself the specific technical proposal is:
The research method that frictional force is contributed in a kind of probe thin slice and each contact zone of substrate, comprising the following steps:
The foundation of step 1, Molecular Dynamics Model
The model system of foundation include simulate atomic force microscope probe needle point absorption a square graphite alkene thin slice and just Spend the single-layer graphene substrate of gradient support.Using the spring mattress bed of normal stiffness k linear increment in X direction by supporter and substrate Each atom of graphene is connected, for analogue probe cantilever, by graphene platelet mass center with spring be connected in X direction with One phantom atom of outside of constant speed 3m/s sliding, the phantom atom are equivalent to cantilever beam.Thin slice and substrate are equal in glide direction It is for sawtooth pattern and wide in the Y direction, and the stacking in a manner of A-B.Graphene-based bottom is having a size of 21.5nm × 6.7nm, lamina dimensions For 6.7nm × 6.7nm, lattice constant 0.142nm, thin slice mass center initial position is located at soft zone domain 1.87nm inclined from substrate mass center Place, 3 column atom of both ends is support boundary to substrate in X direction, its all freedom degree in addition to Z-direction translation is constrained, close to support The 3 column atoms on boundary are temperature adjustment side, and translation and rotation about the z axis, the Y-direction of system of the constraint thin slice along Y-direction are arranged to week Phase property boundary condition.Effect gesture between same layer atom uses Tersoff-Brenner gesture, the effect gesture between thin slice and substrate Using the weaker Lennard-Jones gesture of stiffness of coupling, potential well constant is 3.73 × 10-3EV, equilibrium constant 0.34nm, truncation Radius is 0.884nm.System uses NVT assemblage, i.e., population, volume and temperature are kept constant, and pass through Langevin Temperature adjustment method adjusts temperature to 300K, and time step 0.5fs, sliding total duration is 1.25ns.All simulations all pass through LAMMPS software package is realized and is completed in 1.5ns.
The influence of step 2, rigidity gradient to frictional force
According to model above system, applies the normal plane load of 0.5nN to each atom of thin slice, calculate separately different base The corresponding relationship of average friction force and slip time under mass center rigidity and rigidity gradient below referred to as rubs average friction force Power.The result shows that frictional force is gradually reduced, when slip time is more than 1ns as thin slice is slided to harder region from compared with soft zone domain When, frictional force is held essentially constant, and when mass center constant rigidity, rigidity gradient is bigger, and frictional force decline is more obvious.It establishes Gradient rigidity support system can simulated substrate support constraint under different layers of graphenes, as support stiffness increases, phase Increase when in graphene number of plies, friction energy loss is caused to reduce, when rigidity is more than certain critical value, spring-supported graphene system System is equivalent to graphite, and frictional force no longer reduces, in mass center constant rigidity, friction system when sliding onto 1ns under different-stiffness gradient Number is 0.005, has the identical order of magnitude with existing experiment and simulation result, illustrates the correctness of this model.
Since frictional force is gradually reduced with sliding time on rigidity gradient direction, in order to reflect probe across its with The complexity of interface potential barrier between substrate is particularly important to how to count frictional force.Thin slice and substrate are in glide direction It is sawtooth pattern, the constant sliding speed of connection thin slice phantom atom is 3m/s, and thin slice skidding distance is equal in the unit time, knot Graphene lattice constant 0.142nm and sliding total duration 1.25ns are closed, 3 instantaneous frictional force have been exactly completed in 0.25ns Glutinous-sliding period.Therefore, to average friction force carry out system timing duration take 0.25ns.All error bars are in this method The calculated result standard error of the mean under 5 different random speed seeds.
The research that frictional force is contributed in step 3, thin slice and each contact zone of substrate
Probe adsorbent sheet is divided into 7 by the influence for apparent rigidity gradient and mass center rigidity to frictional force, this method A region (being followed successively by T1~T7 along rigidity augment direction), except T4 is in addition to X-direction includes 22 column atoms, remaining each area includes 1 Column atom.It is equal to 12nN/nm, rigidity gradient equal to 1.34nN/nm in mass center rigidity by analyzing each area2Lower suffered frictional force (Van der Waals force of glide direction) it is found that in entire slipping, frictional force suffered by T1 and T2 is positive, remaining each area's friction Power is negative, and the frictional force absolute value of all dividing regions reduces with the increase of rigidity, and frictional force suffered by T4 is put down It is found after arriving each column atom, frictional force Ti suffered by each area's each column atomf(i takes 1~7, total frictional force) it is ordered as T1f>T2f>0>T5f>T3f>T4f>T6f>T7f.That is, T1fAnd T2fNot only without tribute Frictional force is offered, drives thin slice forward slip, T7 insteadfThe frictional force of contribution is maximum.If the frictional force Zhan by each column atom is total The ratio of frictional force is defined as friction contribution ratio, then in entire slipping, T1fTo the contribution of total frictional force compare for- 36%~-39%, T2fContribution to compare be -7%~-10%.With the increase of support stiffness, T7fTo the contribution ratio of total frictional force Also higher, 47%, about T3 are risen to from 33%f~T6f4~15 times for contributing ratio.
Frictional force be two relative motions the secondary contact surface of friction between various power resultant force.It is respectively connect to clear substrate to thin slice The influence of area's frictional force is touched, this method is equal to 17nN/nm to mass center rigidity respectively, rigidity gradient is equal to 2.68nN/nm2Lower thin slice The atom of S0 and S8 at substrate contact zone S1~S7 (Ti corresponds to Si) and Contact Boundary transition region extension corresponding to each region Vibration amplitude (standard deviation) and normal deformation amount are counted.The result shows that biggish substrate support rigidity can inhibit atom Warm-up movement, while the atomic heat vibration amplitude at S0 and S8 is apparently higher than adjacent contact area, illustrate the thermal vibration of atom not only by The contact squeeze of the constraint of substrate support rigidity, thin slice and substrate can also inhibit the oscillation of atom.Moreover, in Contact Boundary transition Area two sides form asymmetrical deformation.It is poor that asymmetrical deformation is consistently formed at S0 and S8.Therefore, the frictional force of each contact zone is thin The two-part collective effect of normal deformation difference that fold gesture and contact zone between piece and substrate generate.The former is under commensurability contact Hinder different-stiffness on the interface potential barrier and rigidity gradient direction of sliding that potential gradient caused by atom thermal vibration is supported to be coupled As a result, the freedom degree constraint that the latter is Contact Boundary transition region two sides atom is mutated and non-equilibrium boundary caused by asymmetrical deformation Potential barrier, the power for foring rigidity gradient direction is poor, and the two synthesizes frictional force jointly.
Further, step 3 specifically:
Research of the factors of 3.1 interface potential barriers and generation driving force to friction effects
Interface potential barrier height reduces with the increase of rigidity, leads to that power is hindered to be gradually reduced；Meanwhile by described previously, Generate driving effect because being known as on rigidity gradient direction potential gradient caused by atom thermal vibration, Contact Boundary transition in contact zone The freedom degree constraint mutation of area two sides atom and normal direction asymmetrical deformation difference etc., individually below divide each driving influence factor Analysis.
1) potential gradient caused by atom thermal vibration in contact zone.The atomic heat vibration amplitude of substrate support rigidity smaller part compared with Greatly, the atomic heat vibration amplitude of rigidity larger part is smaller, and the difference of this vibration amplitude produces model moral on rigidity gradient direction Magnificent potential energy difference and form driving force.Similar to the thermal driving force of atomic vibration difference in magnitude formation, application electricity on temperature gradient direction The Van der Waals potential energy difference and device fillet transition position thermal vibration difference in magnitude that the heterogeneity hot-fluid for pressing gradient to generate is formed The driving effect of formation, the generation process of driving force is by the potential energy between graphene layerIt illustrates, wherein kvdw For Van der Waals force constant, μiDeviate the displacement of equilbrium position (0.34nm) for i-th of atom.And when support stiffness increases, gesture Driving force caused by gradient reduces, and weakens to the negative function for hindering power.2) freedom degree of Contact Boundary transition region two sides atom Potential gradient caused by constraint is mutated.When substrate support rigidity is identical, support stiffness is identical to the vibration constraint of substrate atoms, by In each probe thin slice atom by uniform normal plane load, the normal deformation of substrate is symmetrical, contact zone boundaries on either side atom Constraint it is also symmetrical, at a certain temperature the amplitude of substrate atoms be in symmetrical concave character type.And when support stiffness change of gradient, The amplitude image of substrate atoms is in asymmetric concave character type.Therefore, thin slice changes the Van der Waals potential energy level of substrate, in thin slice and substrate Effective contact zone, there are a potential wells for the potential energy level of substrate, and the boundary in thin slice and substrate contact zone has clearly Potential energy gradient.The Van der Waals potential energy field of certain point is as common with many atoms similar in the point in substrate in thin slice T1 or T7 It is caused, and a part is limited in effective contact zone, this part of atoms by the extruding of thin slice in these atoms, thermal vibration amplitude It is smaller, and another part atom (such as S0 and S8) at Contact Boundary transition region extension, these atoms are not by the constraint of thin slice And thermal vibration is more violent, the difference of this boundary atomic vibration amplitude can be upwardly formed potential gradient in rigidity gradient side.In fact, Even if the thermal vibration amplitude of the low constraint atom in Contact Boundary two sides is also apparently higher than the region original that is squeezed when rigidity gradient is zero The value of son.When substrate mass center rigidity is smaller, rigidity gradient is larger, contact zone boundaries on either side atom bound difference is obvious, causes The asymmetric concave character type potential energy level potential well of substrate is deeper, so that Interfacial Potential Barrier height is larger, frictional force is larger.And work as substrate When mass center rigidity is larger, support stiffness gradient is smaller, the constraint of contact zone boundaries on either side atom is relatively strong, the difference of thermal vibration amplitude It is unobvious, cause Interfacial Potential Barrier height smaller, boundary friction force is also smaller.3) method of Contact Boundary transition region two sides atom To potential gradient caused by asymmetrical deformation difference.T1 is in softer edge transitional region, and T7, in harder region, the two is in normal direction side Upward deflection is different always, and this asymmetrical deformation difference can also generate driving force, but with the increase of support stiffness, become Shape difference is gradually reduced, and the driving force as caused by modified difference also fades away.
To sum up, on the direction that rigidity gradient increases, there is subtracting for barrier height between generating the secondary interface of friction for hindering power Factors (atom thermal vibration is poor, freedom degree constraint is mutated and asymmetrical deformation is poor) that are small and causing driving effect subtract driving force Small competition coupling.
Research of 3.2 rigidity gradients to the inherent mechanism of each dividing regions friction effects
According to the above theory analysis, in order to probe into and clear rigidity gradient in each dividing regions friction effects of T1~T7 In mechanism, 12nN/nm, 17nN/nm, 22nN/nm are equal to mass center rigidity respectively and rigidity gradient is equal to 1.34nN/nm2、 1.84nN/nm2、2.17nN/nm2、2.68nN/nm2、3.51nN/nm2The Van der Waals force of the area Xia Ge glide direction is calculated.Mould Quasi- result and specific parsing are as follows: 1) under this method mass center rigidity and all values of rigidity gradient, T1fDirection always with Glide direction is consistent, because T1 is in the decline stage in Contact Boundary transition region asymmetrical deformation area, while the pact of transition region atom The potential gradient that beam conditional mutation and support stiffness gradient generate also will form driving force, although in sliding process median surface potential barrier Motion-impeding frictional force can be generated, but biggish driving force is enough to overcome this inhibition and make T1fIn entire mistake Cheng Zhongjun shows as driving force.When substrate mass center rigidity is smaller, rigidity gradient is bigger, T1fIt is bigger and decline in slipping Also it is more obvious.Therefore, biggish driving force is generated by lesser mass center rigidity and biggish rigidity gradient collective effect.2) When mass center rigidity is equal to 12nN/nm, rigidity gradient is equal to 1.34nN/nm2When, T2fPerseverance is positive and increases monotonic decreasing with rigidity, The driving force that juxtaposition metamorphose and rigidity gradient generate at this time is entirely capable of overcoming the obstruction of interface potential barrier.With the increase of rigidity, connect Touching area's deflection and interface potential barrier height decline, and lead to T2fDullness reduces.But it is equal to 12nN/nm, rigidity ladder in mass center rigidity Degree is equal to 1.84nN/nm2When, T2fIt first increased dramatically with the increase of rigidity and then slowly reduce again.Because when rigidity gradient is larger, Initial position where T2 is softer, and higher interface potential barrier counteracts part driving as caused by asymmetrical deformation and rigidity gradient Power, as thin slice is slided to harder region, interface potential barrier height rapid decrease, driving caused by contact zone deformation and rigidity gradient Power accounts for leading, leads to T2fIt steeply rises.Hereafter, as the increase contact zone deflection of rigidity reduces, so that T2fBecome smaller.And work as Mass center rigidity larger (17nN/nm, 22nN/nm) and the also larger (2.68nN/nm of rigidity gradient2、3.51nN/nm2) when, with thin The sliding of piece, T2fIt is initially frictional force, is subsequently changed to driving force monotonic decreasing again.This is because substrate mass center rigidity is larger, Initial position is slided, frictional force caused by interface potential barrier, which is greater than caused by contact zone asymmetrical deformation descending branch and rigidity gradient, drives Power, so that T2fIt is initially obstruction power.But with the increase of rigidity, interface fold gesture reduces, and in 0.5ns, interface potential barrier is It is not enough to offset driving force, becomes T2 stress just.Hereafter, the deflection of asymmetrical deformation area descending branch and barrier height are with rigid The increase of degree and reduce, cause T2fIt gradually becomes smaller.3) the asymmetrical deformation trend of each area two sides T3~T6 slows down, and friction is advocated If interface potential barrier height reduces, friction to overcome shear force caused by the fold gesture of interface, and with the increase of rigidity The absolute value of power reduces.Since T7 is Contact Boundary transition region, contact zone boundaries on either side consistently forms the rising of asymmetrical deformation In the stage, deflection is obvious compared with T3~T6, while the constraint condition mutation of transition region atom can also generate frictional force, and T7 is always It is in harder region, the amplitude for hindering the interface potential barrier height of sliding to reduce when increasing with rigidity is also smaller, therefore, T7fObviously Compared with T3f~T6fGreatly, and with the trend that its value of increase of rigidity reduces also compare mitigation.
In macro-scale, due to very small boundary-contact surface ratio, boundary effect is usually ignored, and in nanoscale, For biggish boundary-contact surface than causing boundary force to have important contribution to friction, this is also that continuum theory cannot be applied The one of the major reasons of atomic scale tribology.
The interlayer Van der Waals potential energy of the reflection mutually nested power of interlayer atom, which externally drives, overcomes interface potential barrier to do work certainly It is set for using.This method calculates mass center rigidity and is equal to 1.84nN/nm equal to 12nN/nm, rigidity gradient2Lower probe thin slice and substrate Van der Waals potential energy between graphene layer.The result shows that with the increase of support stiffness immediately below thin slice mass center, every in 0.25ns Average Van der Waals potential energy PaveExponentially rise.Instantaneous Van der Waals potential energy PinstDifference (i.e. barrier height, adjacent peaks trough it Difference) it is gradually reduced, illustrate that probe is that the obstruction work done of substrate is overcome to be gradually reduced in slipping.This and frictional force with The variation tendency of rigidity is almost the same, is also consistent with correlation theory and experimental result.Rigidity is bigger, gets over to the inhibition of atomic vibration Obviously, interlayer Van der Waals barrier height is lower, and frictional force is smaller.Since each column atom of thin slice is in the graphite of rigidity gradient support On alkenyl bottom, therefore, Van der Waals potential energy suffered by each column atom is different, and what this method calculated is total gesture of thin slice and substrate Can, although cannot reflect the potential energy situation of each column atom of thin slice, the barrier height trend reduced with the increase of support stiffness Be enough to illustrate: when support stiffness difference, interlayer Van der Waals potential energy is different, and the support of substrate rigidity gradient can generate potential gradient.This The potential barrier at place is potential barrier caused by different-stiffness support atom thermal vibration on the interface potential barrier and rigidity gradient direction for hinder sliding Coefficient result.If frictional force and interface potential barrier height are directly proportional, and barrier height is with rigidity when substrate constant rigidity The variation of increase is more gentle, and frictional force is obvious with the variation that rigidity increases, and the two variation tendency is not exactly the same.Cause The reason of this species diversity, is, except potential barrier caused by the interface potential barrier and different-stiffness support atom thermal vibration for hindering probe sliding Outside, in support stiffness smaller area, influence driving force other two factor (Contact Boundary transition region two sides atom it is asymmetric The constraint of the freedom degree of modified difference and edge transitional region two sides atom is poor) it is larger, the driving force of generation is also larger, leads to frictional force Decline is very fast.And when thin slice slides into rigidity large area, the driving force of generation is smaller, and frictional force downward trend is caused to slow down.
Compared with prior art, beneficial effects of the present invention are
1) be equivalent to firstly, changing substrate support rigidity and simulate different layers of graphenes, easy to operate, controllability compared with By force；Secondly as substrate only has one layer of graphene, shared supercomputer resource is smaller during Molecular Dynamics Calculation, to mention The high efficiency for disclosing graphene friction energy loss inherent mechanism.2) when device slips over two different bound base bottoms or Liang Zhong material circle When face, since the difference of elasticity modulus of materials causes supporter to form rigidity gradient in glide direction, and when commensurability contact Van der Waals potential energy between interface is small, and contact is stablized, and the secondary interface of two frictions is usually contacted in a manner of commensurability.So in conjunction with rigidity The driving force and commensurability that gradient induces, which contact, hinders the sliding behavior of power research nano-device very caused by lower interface fold gesture It is important.And commensurability contact and substrate support rigidity gradient between graphene layer are changed into the relative motion combined, domestic and foreign scholars Rarely has research.Therefore, research substrate support rigidity gradient changes the influence to frictional force, with important science and reality meaning Justice.
Detailed description of the invention
The graphene model of Fig. 1 (a) spring mattress bed rigidity gradient support；
Fig. 1 (b) graphene platelet-substrate Frictional Slipping model；
The variation relation of Fig. 2 average friction force and rigidity gradient；
Each Division schematic diagram of Fig. 3 thin slice；
Frictional force suffered by each dividing regions of Fig. 4 thin slice；
The thermal vibration amplitude of each contact zone atom of Fig. 5 (a) substrate；
The normal deformation amount of each contact zone atom of Fig. 5 (b) substrate；
Frictional force suffered by the area Fig. 6 (a) thin slice T1；
Frictional force suffered by the area Fig. 6 (b) thin slice T2；
Frictional force suffered by the area Fig. 6 (c) thin slice T3；
Frictional force suffered by the area Fig. 6 (d) thin slice T4；
Frictional force suffered by the area Fig. 6 (e) thin slice T6；
Frictional force suffered by the area Fig. 6 (f) thin slice T7；
Fig. 7 (a) interlayer be averaged Van der Waals potential energy glide direction variation tendency；
Variation tendency of the instantaneous Van der Waals potential energy of Fig. 7 (b) interlayer in glide direction.
Specific embodiment
Technical solution of the present invention is described in more detail below with reference to specific drawings and examples.
1, Molecular Dynamics Model
The model system that this method is established includes simulation atomic force microscope (atomic force microscope, brief note The single-layer graphene substrate for a square graphite alkene thin slice and the rigidity gradient support adsorbed for AFM) probe tip, as shown in Figure 1. Supporter is connected by the spring mattress bed using normal stiffness k linear increment in X direction with each atom of substrate graphene.In order to Graphene platelet mass center is connected in X direction with spring with the virtual original in the outside one of constant speed 3m/s sliding by analogue probe cantilever Sub (being equivalent to cantilever beam), thin slice and substrate are sawtooth pattern (i.e. commensurability contacts) and wide in the Y direction in glide direction, and The stacking in a manner of A-B.Graphene-based bottom having a size of 21.5nm × 6.7nm (5632 atoms), lamina dimensions be 6.7nm × 6.7nm (1792 atoms), lattice constant 0.142nm, thin slice mass center initial position are located at from the inclined soft zone domain of substrate mass center 1.87nm place.3 column atom of both ends is support boundary to substrate in X direction, constrains its all freedom degree in addition to Z-direction translation, tightly The 3 column atoms on adjacent support boundary are temperature adjustment side, and translation and rotation about the z axis, the Y-direction of system of the constraint thin slice along Y-direction are set It is set to periodic boundary condition.Effect gesture between same layer atom uses Tersoff-Brenner gesture, between thin slice and substrate The gesture Lennard-Jones gesture weaker using stiffness of coupling is acted on, potential well constant is 3.73 × 10-3EV, the equilibrium constant are 0.34nm, truncation radius 0.884nm.System uses NVT assemblage, i.e., population, volume and temperature are kept constant, and are led to It crosses Langevin temperature adjustment method and adjusts temperature to 300K, time step 0.5fs, sliding total duration is 1.25ns.All simulations It is all to be realized by LAMMPS software package and completed in 1.5ns.
2, influence of the rigidity gradient to frictional force
According to model above system, applies the normal plane load of 0.5nN to each atom of thin slice, calculate separately different base Mass center rigidity (midpoint stiffness, be abbreviated as m) and rigidity gradient (stiffness gradient is abbreviated as g, and) under average friction force FfWith the corresponding relationship of slip time T, average friction force is referred to as frictional force below.As a result Showing to slide from compared with soft zone domain to harder region with thin slice, frictional force is gradually reduced, when slip time is more than 1ns, friction Power is held essentially constant.And as m=12nN/nm, g is bigger, and the fall of frictional force is bigger.For example, working as g= 1.34nN/nm2When, FfDrop to 3.65nN from 6.50nN；G=1.84nN/nm2When, FfDrop to 4.78nN from 22.26nN, bears Number indicate frictional force it is opposite with glide direction.The reason of leading to the above variation is the gradient rigidity support system energy that this method is established Different layers of graphenes under enough simulated substrate support constraints are equivalent to graphene number of plies increase, lead as support stiffness increases Friction energy loss is caused to reduce, when rigidity is more than certain critical value, spring-supported graphene system is equivalent to graphite, and frictional force is not Reduce again.Coefficient of friction is 0.005 when sliding onto 1ns under the conditions of both the above, has phase with existing experiment and simulation result The same order of magnitude, illustrates the correctness of this model.
Since frictional force is gradually reduced with sliding time on rigidity gradient direction, in order to reflect probe across its with The complexity of interface potential barrier between substrate is particularly important to how to count frictional force.Thin slice and substrate are in glide direction It is sawtooth pattern, the constant sliding speed of connection thin slice phantom atom is 3m/s, and thin slice skidding distance is equal in the unit time, knot Graphene lattice constant 0.142nm and sliding total duration 1.25ns are closed, 3 instantaneous frictional force have been exactly completed in 0.25ns Glutinous-sliding period.Therefore, to average friction force carry out system timing duration take 0.25ns.All error bars are in this method The calculated result standard error of the mean under 5 different random speed seeds.
3, the contribution of thin slice and each contact zone of substrate to frictional force
Probe adsorbent sheet is divided into 7 by the influence for apparent rigidity gradient and mass center rigidity to frictional force, this method A region (being followed successively by T1~T7 along rigidity augment direction), except T4 (1408 atoms) X-direction include 22 column atoms in addition to, remaining Each area's (64 atoms) includes 1 column atom, as shown in Figure 3.By analyzing each area in m=12nN/nm, g=1.34nN/nm2 It is found that in entire slipping, frictional force suffered by T1 and T2 is positive for lower suffered frictional force (Van der Waals force of X-direction), Remaining each area's frictional force is negative, and the frictional force absolute value of all dividing regions reduces with the increase of rigidity, by T4 institute The frictional force received finds after averagely arriving each column atom, frictional force Ti suffered by each area's each column atomf(i takes 1~7, total frictional force) it is ordered as T1f>T2f>0>T5f>T3f>T4f>T6f>T7f, as shown in Figure 4.That is, T1fAnd T2f Not only without contribution frictional force, thin slice forward slip, T7 are driven insteadfThe frictional force of contribution is maximum.If by each column atom The ratio that frictional force accounts for total frictional force is defined as friction contribution ratio, then in entire slipping, T1fTribute to total frictional force It offers than for -36%~-39%, T2fContribution to compare be -7%~-10%.With the increase of support stiffness, T7fAccount for total frictional force Ratio is also higher, rises to 47%, about T3 from 33%f~T6fZhan always rubs 4~15 times of ratio.
Frictional force be two relative motions the secondary contact surface of friction between various power resultant force.It is respectively connect to clear substrate to thin slice The influence of area's frictional force is touched, this method is respectively to m=17nN/nm, g=2.68nN/nm2Substrate corresponding to lower each region of thin slice Atomic vibration amplitude (standard deviation) AF of S0 and S8 at contact zone S1~S7 (Ti corresponds to Si) and Contact Boundary transition region extension It is counted with normal deformation amount, as shown in Figure 5.The result shows that biggish substrate support rigidity can inhibit the warm-up movement of atom, The atomic heat vibration amplitude at S0 and S8 is apparently higher than adjacent contact area simultaneously, illustrates the thermal vibration of atom not only by substrate support The contact squeeze of the constraint of rigidity, thin slice and substrate can also inhibit the oscillation of atom；Moreover, in Contact Boundary transition region two sides (in figure at ellipse) forms asymmetrical deformation, and Fig. 5 (b) is the evolutionary process of normal direction asymmetrical deformation amount in slipping, by Figure is it is found that consistently form asymmetrical deformation at S0 and S8 poor.Therefore, the frictional force of each contact zone is the pleat between thin slice and substrate The two-part collective effect of normal deformation difference that gesture of wrinkling and contact zone generate.The former is the lower interfacial potential for hindering sliding of commensurability contact Build and rigidity gradient direction on different-stiffness support atom thermal vibration caused by potential gradient be coupled as a result, the latter is contact edge Non-equilibrium boundary potential barrier caused by the freedom degree constraint mutation of boundary transition region two sides atom and asymmetrical deformation forms rigidity ladder The power for spending direction is poor, and the two synthesizes frictional force jointly.
Influence of the factors of 3.1 interface potential barriers and generation driving force to frictional force
Interface potential barrier height reduces with the increase of rigidity, leads to that power is hindered to be gradually reduced；Meanwhile by described previously, Generate driving effect because being known as on rigidity gradient direction potential gradient caused by atom thermal vibration, Contact Boundary transition in contact zone The freedom degree constraint mutation of area two sides atom and normal direction asymmetrical deformation difference etc., individually below divide each driving influence factor Analysis.
1) potential gradient caused by atom thermal vibration in contact zone.The atomic heat vibration amplitude of substrate support rigidity smaller part compared with Greatly, the atomic heat vibration amplitude of rigidity larger part is smaller, and the difference of this vibration amplitude produces model moral on rigidity gradient direction Magnificent potential energy difference and form driving force, similar on temperature gradient direction atomic vibration difference in magnitude formed thermal driving force, apply electricity The Van der Waals potential energy difference and device fillet transition position thermal vibration difference in magnitude that the heterogeneity hot-fluid for pressing gradient to generate is formed The driving effect of formation, the generation process of driving force is by the potential energy between graphene layerIt illustrates, wherein kvdw For Van der Waals force constant, μiDeviate the displacement of equilbrium position (0.34nm) for i-th of atom.And when support stiffness increases, gesture Driving force caused by gradient reduces, and weakens to the negative function for hindering power.2) freedom degree of Contact Boundary transition region two sides atom Potential gradient caused by constraint is mutated.When substrate support rigidity is identical, support stiffness is identical to the vibration constraint of substrate atoms, by In each probe thin slice atom by uniform normal plane load, the normal deformation of substrate is symmetrical, contact zone boundaries on either side atom Constraint it is also symmetrical, at a certain temperature the amplitude of substrate atoms be in symmetrical concave character type.And when support stiffness change of gradient, The amplitude image of substrate atoms is in asymmetric concave character type, as shown in Fig. 5 (a).Therefore, thin slice changes the Van der Waals potential energy of substrate Face, in effective contact zone of thin slice and substrate, there are a potential wells for the potential energy level of substrate, and on the side of thin slice and substrate contact zone There is obviously potential energy gradient at boundary.The Van der Waals potential energy field of certain point is by close with the point in substrate in thin slice T1 or T7 Many atoms jointly caused by, and a part is in effective contact zone, extruding of this part of atoms by thin slice in these atoms Limitation, thermal vibration amplitude is smaller, and another part atom (such as S0 and S8) at Contact Boundary transition region extension, these atoms Not by the constraint of thin slice, thermal vibration is more violent, the difference of this boundary atomic vibration amplitude can on rigidity gradient direction shape At potential gradient.Even if when rigidity gradient is zero, Contact Boundary two sides it is low constraint atom thermal vibration amplitude be also apparently higher than by The value of crush-zone atom.When substrate mass center rigidity is smaller, rigidity gradient is larger, contact zone boundaries on either side atom bound difference is bright It is aobvious, cause the asymmetric concave character type potential energy level potential well of substrate deeper, so that Interfacial Potential Barrier height is larger, frictional force is larger. And when substrate mass center rigidity is larger, support stiffness gradient is smaller, the constraint of contact zone boundaries on either side atom is relatively strong, thermal vibration The difference of amplitude is unobvious, causes barrier height smaller, boundary friction force is also smaller.3) method of Contact Boundary transition region two sides atom To potential gradient caused by asymmetrical deformation difference.T1 is in softer edge transitional region, and T7 is in harder region, by drilling for Fig. 5 (b) For change process it is found that deflection of the two in normal orientation is different always, this asymmetrical deformation difference can also generate driving force, but It is the increase with support stiffness, modified difference is gradually reduced, and the driving force as caused by modified difference also fades away.
To sum up, on the direction that rigidity gradient increases, there is subtracting for barrier height between generating the secondary interface of friction for hindering power Factors (atom thermal vibration is poor, freedom degree constraint is mutated and asymmetrical deformation is poor) that are small and causing driving effect subtract driving force Small competition coupling.
Inherent mechanism of 3.2 rigidity gradients to each dividing regions friction effects
According to the above theory analysis, in order to probe into and clear rigidity gradient in each dividing regions friction effects of T1~T7 In mechanism, respectively to m=12nN/nm, 17nN/nm, 22nN/nm and g=1.34nN/nm2、1.84nN/nm2、2.17nN/ nm2、2.68nN/nm2、3.51nN/nm2The Van der Waals force of the area Xia Ge X-direction is calculated, and (is omitted as shown in Fig. 6 (a)~(f) T5f).Analog result and specific parsing are as follows: 1) under all values of this method m and g, T1fDirection with glide direction one It causes, because T1 is in the decline stage in Contact Boundary transition region asymmetrical deformation area, while the constraint condition mutation of transition region atom And the potential gradient that support stiffness gradient generates also will form driving force, although obstruction can be generated in sliding process median surface potential barrier The frictional force of movement, but biggish driving force is enough to overcome this inhibition and make T1fIt shows in the whole process For driving force.When substrate mass center rigidity is smaller, rigidity gradient is bigger, T1fIt is bigger and decline in slipping and be also more obvious.Cause This, biggish driving force is generated by lesser mass center rigidity and biggish rigidity gradient collective effect.2) work as m=12nN/ Nm, g=1.34nN/nm2When, T2fPerseverance is positive and increases monotonic decreasing with rigidity, and juxtaposition metamorphose and rigidity gradient generate at this time Driving force is entirely capable of overcoming the obstruction of interface potential barrier.With the increase of rigidity, contact zone deflection and interface potential barrier height under Drop, leads to T2fDullness reduces.But in m=12nN/nm, g=1.84nN/nm2When, T2fWith the increase of rigidity first increased dramatically with Slowly reduce again afterwards.Because when g is larger, the initial position where T2 is softer, higher interface potential barrier counteracts part by non-right Claim driving force caused by deformation and rigidity gradient, as thin slice is slided to harder region, interface potential barrier height rapid decrease, contact Driving force caused by area's deformation and rigidity gradient accounts for leading, leads to T2fIt steeply rises.Hereafter, with the increase contact zone of rigidity Deflection reduces, so that T2fBecome smaller.And work as m larger (17nN/nm, 22nN/nm) and the also larger (2.68nN/nm of g2、3.51nN/ nm2) when, with the sliding of thin slice, T2fIt is initially frictional force, is subsequently changed to driving force monotonic decreasing again.This is because substrate matter Heart rigidity is larger, and the frictional force caused by sliding initial position, interface potential barrier is greater than contact zone asymmetrical deformation descending branch and just Driving force caused by gradient is spent, so that T2fIt is initially obstruction power.But with the increase of rigidity, interface fold gesture reduces, When 0.5ns, interface potential barrier has been not enough to offset driving force, becomes T2 stress just.Hereafter, the deformation of asymmetrical deformation area descending branch Amount and barrier height reduce with the increase of rigidity, cause T2fIt gradually becomes smaller.3) asymmetrical deformation of each area two sides T3~T6 Trend slows down, and frictional force is mainly to overcome shear force caused by the fold gesture of interface, and with the increase of rigidity, interface Barrier height reduces, and the absolute value of frictional force reduces.Since T7 is Contact Boundary transition region, contact zone boundaries on either side is consistently formed The ascent stage of asymmetrical deformation, deflection is obvious compared with T3~T6, while the constraint condition mutation of transition region atom can also generate Frictional force, and T7 has been at harder region, the amplitude for hindering the interface potential barrier height of sliding to reduce when increasing with rigidity It is smaller, therefore, T7fObviously compared with T3f~T6fGreatly, and with the trend that its value of increase of rigidity reduces also compare mitigation.
In macro-scale, due to very small boundary-contact surface ratio, boundary effect is usually ignored, and in nanoscale, For biggish boundary-contact surface than causing boundary force to have important contribution to friction, this is also that continuum theory cannot be applied The one of the major reasons of atomic scale tribology.
The interlayer Van der Waals potential energy of the reflection mutually nested power of interlayer atom, which externally drives, overcomes interface potential barrier to do work certainly It is set for using.This method calculates m=12nN/nm, g=1.84nN/nm2Van der Waals between lower probe thin slice and substrate graphene layer Potential energy, as shown in Figure 7.The result shows that with the increase of support stiffness immediately below thin slice mass center, every the average model in 0.25ns Moral China potential energy PaveExponentially rise (Fig. 7 (a))；Instantaneous Van der Waals potential energy PinstDifference (i.e. barrier height, adjacent peaks trough it Difference) it is gradually reduced (Fig. 7 (b)), illustrate that probe is that the obstruction work done of substrate is overcome to be gradually reduced in slipping.This and Frictional force is almost the same with the variation tendency of rigidity in Fig. 2, is also consistent with correlation theory and experimental result.Rigidity is bigger, to original The inhibition of son vibration is more obvious, and interlayer Van der Waals barrier height is lower, and frictional force is smaller.Since each column atom of thin slice is in rigidity On the graphene-based bottom of gradient support, therefore, Van der Waals potential energy suffered by each column atom is different, and what this method calculated is thin Total potential energy of piece and substrate, although cannot reflect the potential energy situation of each column atom of thin slice, barrier height with support stiffness increasing Big and reduceds trend is enough to illustrate: when support stiffness difference, interlayer Van der Waals potential energy is different, and substrate rigidity gradient supports can Generate potential gradient.Potential barrier herein is different-stiffness support atomic heat vibration on the interface potential barrier and rigidity gradient direction for hinder sliding The coefficient result of both potential barriers caused by dynamic.If frictional force and interface potential barrier height are at just when substrate constant rigidity Than, and the variation that barrier height increases with rigidity in Fig. 7 (b) is more gentle, the variation that frictional force increases with rigidity in Fig. 2 is but compared Obviously, the two variation tendency is not exactly the same.The reason of leading to this species diversity, is, except the interface potential barrier for hindering probe sliding and not It is supported outside potential barrier caused by atom thermal vibration with rigidity, in support stiffness smaller area, influences other two factor of driving force (the asymmetrical deformation difference of Contact Boundary transition region two sides atom and the constraint of the freedom degree of edge transitional region two sides atom are poor) compared with Greatly, the driving force of generation is also larger, causes frictional force decline very fast.And when thin slice slides into rigidity large area, the drive of generation Power is smaller, and frictional force downward trend is caused to slow down.
The foregoing is only a preferred embodiment of the present invention, the scope of protection of the present invention is not limited to this, it is any ripe Know those skilled in the art within the technical scope of the present disclosure, the letter for the technical solution that can be become apparent to Altered or equivalence replacement are fallen within the protection scope of the present invention.

Claims (3)

1. the research method that frictional force is contributed in a kind of probe thin slice and each contact zone of substrate, which is characterized in that including following step It is rapid:
The foundation of step 1, Molecular Dynamics Model
The model system of foundation includes the square graphite alkene thin slice and rigidity ladder for simulating the absorption of atomic force microscope probe needle point Spend the single-layer graphene substrate of support；Using the spring mattress bed of normal stiffness k linear increment in X direction by supporter and substrate graphite Each atom of alkene is connected, and for analogue probe cantilever, graphene platelet mass center is connected in X direction with spring with constant speed One phantom atom of outside of 3m/s sliding, the phantom atom are equivalent to cantilever beam；Thin slice and substrate are saw in glide direction Flute profile and wide in the Y direction, and the stacking in a manner of A-B；Graphene-based bottom is having a size of 21.5nm × 6.7nm, lamina dimensions 6.7nm × 6.7nm, lattice constant 0.142nm, thin slice mass center initial position are located at soft zone domain 1.87nm inclined from substrate mass center Place, 3 column atom of both ends is support boundary to substrate in X direction, its all freedom degree in addition to Z-direction translation is constrained, close to support The 3 column atoms on boundary are temperature adjustment side, and translation and rotation about the z axis, the Y-direction of system of the constraint thin slice along Y-direction are arranged to week Phase property boundary condition；Effect gesture between same layer atom uses Tersoff-Brenner gesture, the effect gesture between thin slice and substrate Using the weaker Lennard-Jones gesture of stiffness of coupling, potential well constant is 3.73 × 10-3EV, equilibrium constant 0.34nm, truncation Radius is 0.884nm；System uses NVT assemblage, i.e., population, volume and temperature are kept constant, and pass through Langevin Temperature adjustment method adjusts temperature to 300K, and time step 0.5fs, sliding total duration is 1.25ns；All simulations all pass through LAMMPS software package is realized and is completed in 1.5ns；
The influence of step 2, rigidity gradient to frictional force
According to model above system, applies the normal plane load of 0.5nN to each atom of thin slice, calculate separately different base mass center The corresponding relationship of average friction force and slip time, is referred to as frictional force for average friction force below under rigidity and rigidity gradient； The result shows that frictional force is gradually reduced as thin slice is slided to harder region from compared with soft zone domain, when slip time is more than 1ns, Frictional force is held essentially constant, and when mass center constant rigidity, rigidity gradient is bigger, and frictional force decline is more obvious；It establishes Gradient rigidity support system can simulated substrate support constraint under different layers of graphenes, as support stiffness increases, quite Increase in graphene number of plies, friction energy loss is caused to reduce, when rigidity is more than certain critical value, spring-supported graphene system It is equivalent to graphite, frictional force no longer reduces, in mass center constant rigidity, coefficient of friction when sliding onto 1ns under different-stiffness gradient It is 0.005, has the identical order of magnitude with existing experiment and simulation result, illustrate the correctness of this model；
Since frictional force is gradually reduced with sliding time on rigidity gradient direction, in order to reflect probe across itself and substrate Between interface potential barrier complexity, be particularly important to how to count frictional force；Thin slice and substrate are in glide direction Sawtooth pattern, the constant sliding speed of connection thin slice phantom atom is 3m/s, and thin slice skidding distance is equal in the unit time, in conjunction with stone Black alkene lattice constant 0.142nm and sliding total duration 1.25ns, it is glutinous-sliding to be exactly completed 3 instantaneous frictional force in 0.25ns Period；Therefore, to average friction force carry out system timing duration take 0.25ns；All error bars are at 5 in this method Calculated result standard error of the mean under different random speed seed；
The research that frictional force is contributed in step 3, thin slice and each contact zone of substrate
Probe adsorbent sheet is divided into 7 areas by the influence for apparent rigidity gradient and mass center rigidity to frictional force, this method Domain is followed successively by T1~T7 along rigidity augment direction, except T4 is in addition to X-direction includes 22 column atoms, remaining each area includes 1 column original Son；It is equal to 12nN/nm, rigidity gradient equal to 1.34nN/nm in mass center rigidity by analyzing each area2Lower suffered frictional force, It is exactly that the Van der Waals force of glide direction is learnt, in entire slipping, frictional force suffered by T1 and T2 is positive, remaining each area rubs It wipes power to be negative, and the frictional force absolute value of all dividing regions reduces with the increase of rigidity, by frictional force suffered by T4 It is found after averagely arriving each column atom, frictional force Ti suffered by each area's each column atomfIt is ordered as T1f>T2f>0>T5f>T3f>T4f>T6f >T7f, i takes 1~7, total frictional forceThat is, T1fAnd T2fNot only without contribution frictional force, instead Drive thin slice forward slip, T7fThe frictional force of contribution is maximum；If the ratio that the frictional force of each column atom accounts for total frictional force determined Justice is friction contribution ratio, then in entire slipping, T1fThe contribution of total frictional force is compared for -36%~-39%, T2f's Contribution is than being -7%~-10%；With the increase of support stiffness, T7fIt is higher than also to the contribution of total frictional force, rise from 33% To 47%, about T3f~T6f4~15 times for contributing ratio；
Frictional force be two relative motions the secondary contact surface of friction between various power resultant force；In order to clear substrate to each contact zone of thin slice The influence of frictional force, this method is equal to 17nN/nm to mass center rigidity respectively, rigidity gradient is equal to 2.68nN/nm2Lower each area of thin slice The atomic vibration amplitude and normal direction of S0 and S8 at substrate contact zone S1~S7 corresponding to domain and Contact Boundary transition region extension Deflection is counted, and Si is corresponded to by Ti herein；The result shows that biggish substrate support rigidity can inhibit the warm-up movement of atom, The atomic heat vibration amplitude at S0 and S8 is apparently higher than adjacent contact area simultaneously, illustrates the thermal vibration of atom not only by substrate support The contact squeeze of the constraint of rigidity, thin slice and substrate can also inhibit the oscillation of atom；Moreover, in Contact Boundary transition region two sides shape At asymmetrical deformation；It is poor that asymmetrical deformation is consistently formed at S0 and S8；Therefore, the frictional force of each contact zone is thin slice and substrate Between the two-part collective effect of normal deformation difference that generates of fold gesture and contact zone；The former, which is that commensurability contact is lower, hinders sliding Interface potential barrier and rigidity gradient direction on different-stiffness support atom thermal vibration caused by potential gradient be coupled as a result, the latter The freedom degree constraint mutation for being Contact Boundary transition region two sides atom and non-equilibrium boundary potential barrier caused by asymmetrical deformation, form The power in rigidity gradient direction is poor, and the two synthesizes frictional force jointly.
2. the research method that frictional force is contributed in probe thin slice according to claim 1 and each contact zone of substrate, feature It is, step 3 specifically:
Research of the factors of 3.1 interface potential barriers and generation driving force to friction effects
Interface potential barrier height reduces with the increase of rigidity, leads to that power is hindered to be gradually reduced；Meanwhile by described previously, generation Driving effect because being known as on rigidity gradient direction potential gradient caused by atom thermal vibration, Contact Boundary transition region two in contact zone The freedom degree constraint mutation of side atom and normal direction asymmetrical deformation difference etc., each driving influence factor play the size of frictional force and determine Effect；
Research of 3.2 rigidity gradients to the inherent mechanism of each dividing regions friction effects
According to the above theory analysis, in order to probe into and clear rigidity gradient to the inherent machine of each dividing regions friction effects of T1~T7 Reason is equal to 12nN/nm, 17nN/nm, 22nN/nm to mass center rigidity respectively and rigidity gradient is equal to 1.34nN/nm2、 1.84nN/nm2、2.17nN/nm2、2.68nN/nm2、3.51nN/nm2The Van der Waals force of the area Xia Ge glide direction is calculated；Mould Quasi- result and specific parsing are as follows: 1) under this method mass center rigidity and all values of rigidity gradient, T1fDirection always with Glide direction is consistent, because T1 is in the decline stage in Contact Boundary transition region asymmetrical deformation area, while the pact of transition region atom The potential gradient that beam conditional mutation and support stiffness gradient generate also will form driving force, although in sliding process median surface potential barrier Motion-impeding frictional force can be generated, but biggish driving force is enough to overcome this inhibition and make T1fIn entire mistake Cheng Zhongjun shows as driving force；When substrate mass center rigidity is smaller, rigidity gradient is bigger, T1fIt is bigger and decline in slipping Also it is more obvious；Therefore, biggish driving force is generated by lesser mass center rigidity and biggish rigidity gradient collective effect；2) When mass center rigidity is equal to 12nN/nm, rigidity gradient is equal to 1.34nN/nm2When, T2fPerseverance is positive and increases monotonic decreasing with rigidity, The driving force that juxtaposition metamorphose and rigidity gradient generate at this time is entirely capable of overcoming the obstruction of interface potential barrier；With the increase of rigidity, connect Touching area's deflection and interface potential barrier height decline, and lead to T2fDullness reduces；But it is equal to 12nN/nm, rigidity ladder in mass center rigidity Degree is equal to 1.84nN/nm2When, T2fIt first increased dramatically with the increase of rigidity and then slowly reduce again；Because when rigidity gradient is larger, Initial position where T2 is softer, and higher interface potential barrier counteracts part driving as caused by asymmetrical deformation and rigidity gradient Power, as thin slice is slided to harder region, interface potential barrier height rapid decrease, driving caused by contact zone deformation and rigidity gradient Power accounts for leading, leads to T2fIt steeply rises；Hereafter, as the increase contact zone deflection of rigidity reduces, so that T2fBecome smaller；And work as When mass center rigidity is larger, such as 17nN/nm, 22nN/nm, and when rigidity gradient is also larger, such as 2.68nN/nm2、3.51nN/nm2, with The sliding of thin slice, T2fIt is initially frictional force, is subsequently changed to driving force monotonic decreasing again；This is because substrate mass center rigidity compared with Greatly, the frictional force caused by sliding initial position, interface potential barrier is greater than contact zone asymmetrical deformation descending branch and rigidity gradient draws The driving force risen, so that T2fIt is initially obstruction power；But with the increase of rigidity, interface fold gesture reduces, in 0.5ns, interface Potential barrier has been not enough to offset driving force, becomes T2 stress just；Hereafter, the deflection and barrier height of asymmetrical deformation area descending branch Reduce with the increase of rigidity, causes T2fIt gradually becomes smaller；3) the asymmetrical deformation trend of each area two sides T3~T6 slows down, and rubs If wiping is advocated to overcome shear force caused by the fold gesture of interface, and with the increase of rigidity, interface potential barrier height subtracts Small, the absolute value of frictional force reduces；Since T7 is Contact Boundary transition region, contact zone boundaries on either side consistently forms asymmetrical deformation Ascent stage, deflection is obvious compared with T3~T6, at the same transition region atom constraint condition mutation can also generate frictional force, and T7 has been at harder region, and the amplitude for hindering the interface potential barrier height of sliding to reduce when increasing with rigidity is also smaller, therefore, T7fObviously compared with T3f~T6fGreatly, and with the trend that its value of increase of rigidity reduces also compare mitigation；
In macro-scale, due to very small boundary-contact surface ratio, boundary effect is usually ignored, and in nanoscale, it is larger Boundary-contact surface than cause boundary force to friction have important contribution, this is also that continuum theory cannot be applied in atom The one of the major reasons of scale tribology；
Reflection mutually nested power of interlayer atom interlayer Van der Waals potential energy externally drive overcome interface potential barrier done work determine work With；This method calculates mass center rigidity and is equal to 1.84nN/nm equal to 12nN/nm, rigidity gradient2Lower probe thin slice and substrate graphite The Van der Waals potential energy of alkene interlayer；The result shows that with the increase of support stiffness immediately below thin slice mass center, every flat in 0.25ns Equal Van der Waals potential energy PaveExponentially rise；Instantaneous Van der Waals potential energy PinstDifference be barrier height i.e. adjacent peaks trough it Difference is gradually reduced, and illustrates that probe is that the obstruction work done of substrate is overcome to be gradually reduced in slipping；This and frictional force with The variation tendency of rigidity is almost the same, is also consistent with correlation theory and experimental result；Rigidity is bigger, gets over to the inhibition of atomic vibration Obviously, interlayer Van der Waals barrier height is lower, and frictional force is smaller；Since each column atom of thin slice is in the graphite of rigidity gradient support On alkenyl bottom, therefore, Van der Waals potential energy suffered by each column atom is different, and what this method calculated is total gesture of thin slice and substrate Can, although cannot reflect the potential energy situation of each column atom of thin slice, the barrier height trend reduced with the increase of support stiffness Be enough to illustrate: when support stiffness difference, interlayer Van der Waals potential energy is different, and the support of substrate rigidity gradient can generate potential gradient；This The potential barrier at place is potential barrier caused by different-stiffness support atom thermal vibration on the interface potential barrier and rigidity gradient direction for hinder sliding Coefficient result；If frictional force and interface potential barrier height are directly proportional, and barrier height is with rigidity when substrate constant rigidity The variation of increase is more gentle, and frictional force is obvious with the variation that rigidity increases, and the two variation tendency is not exactly the same；Cause The reason of this species diversity, is, except potential barrier caused by the interface potential barrier and different-stiffness support atom thermal vibration for hindering probe sliding Outside, in support stiffness smaller area, influence other two factor of driving force: Contact Boundary transition region two sides atom it is asymmetric The freedom degree of modified difference and edge transitional region two sides atom constraint difference is larger, and the driving force of generation is also larger, leads to frictional force Decline is very fast；And when thin slice slides into rigidity large area, the driving force of generation is smaller, and frictional force downward trend is caused to slow down.
3. the research method that frictional force is contributed in probe thin slice according to claim 2 and each contact zone of substrate, feature It is, in step 3.1, contribution of each driving influence factor to frictional force specifically:
1) potential gradient caused by atom thermal vibration in contact zone；The atomic heat vibration amplitude of substrate support rigidity smaller part is larger, The atomic heat vibration amplitude of rigidity larger part is smaller, and the difference of this vibration amplitude produces Van der Waals gesture on rigidity gradient direction Energy is poor and forms driving force；Similar to the thermal driving force of atomic vibration difference in magnitude formation, application voltage ladder on temperature gradient direction The Van der Waals potential energy difference and device fillet transition position thermal vibration difference in magnitude that the heterogeneity hot-fluid that degree generates is formed are formed Driving effect, the generation process of driving force is by the potential energy between graphene layerIt illustrates, wherein kvdwFor model Moral China force constant, μiDeviate the displacement of equilbrium position for i-th of atom；And when support stiffness increases, it is driven caused by potential gradient Power reduces, and weakens to the negative function for hindering power；2) the freedom degree constraint mutation of Contact Boundary transition region two sides atom causes Potential gradient；When substrate support rigidity is identical, support stiffness is identical to the vibration constraint of substrate atoms, since each probe is thin For piece atom by uniform normal plane load, the normal deformation of substrate is symmetrical, and the constraint of contact zone boundaries on either side atom is also symmetrical, The amplitude of substrate atoms is in symmetrical concave character type at a certain temperature；And when support stiffness change of gradient, the vibration of substrate atoms Width figure is in asymmetric concave character type；Therefore, thin slice changes the Van der Waals potential energy level of substrate, in effective contact of thin slice and substrate Area, there are a potential wells for the potential energy level of substrate, and the boundary in thin slice and substrate contact zone has obviously potential energy gradient； In thin slice T1 or T7 the Van der Waals potential energy field of certain point be as in substrate with many atoms similar in the point jointly caused by, and this A part is limited in effective contact zone, this part of atoms by the extruding of thin slice in a little atoms, and thermal vibration amplitude is smaller, and in addition A part of atom is at Contact Boundary transition region extension, and such as S0 and S8, these atoms are not by the constraint of thin slice and thermal vibration is more acute Strong, the difference of this boundary atomic vibration amplitude can be upwardly formed potential gradient in rigidity gradient side；In fact, even if in rigidity ladder When degree is zero, the thermal vibration amplitude of the low constraint atom in Contact Boundary two sides is also apparently higher than the value for the region atom that is squeezed；Work as base When substrate heart rigidity is smaller, rigidity gradient is larger, contact zone boundaries on either side atom bound difference is obvious, leads to the asymmetric of substrate Concave character type potential energy level potential well is deeper, so that Interfacial Potential Barrier height is larger, frictional force is larger；And when substrate mass center rigidity compared with Greatly, when support stiffness gradient is smaller, the constraint of contact zone boundaries on either side atom is relatively strong, and the difference of thermal vibration amplitude is unobvious, leads Cause Interfacial Potential Barrier height smaller, boundary friction force is also smaller；3) normal direction of Contact Boundary transition region two sides atom is asymmetric Potential gradient caused by modified difference；T1 is in softer edge transitional region, and T7 is in harder region, change of the two in normal orientation Shape amount is different always, and this asymmetrical deformation difference can also generate driving force, but with the increase of support stiffness, modified difference is gradually Reduce, the driving force as caused by modified difference also fades away；
To sum up, on the direction that rigidity gradient increases, exist between generating the secondary interface of friction for hindering power the reduction of barrier height and The poor factors atom thermal vibration of driving effect, freedom degree constraint mutation and asymmetrical deformation official post driving force is caused to reduce competing Strive coupling.
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