Frenkel-Kontorova模型中垫底势对最大静摩擦力的影响

用一维Frenkel-Kontorova模型,对相互接触的两个单原子分子链具有相对运动趋势时所产生的最大静摩擦力进行了研究.分别在相邻原子的距离与周期势场的周期比b/a为可公度(commensurate)、黄金分割(golden mean)、螺旋分割(spiral mean)三种情况下,描述了特殊垫底势力的振幅A与分子链静摩擦力的关系,在特殊垫底势力的作用下上层原子链弹性系数K对静摩擦力的影响.研究表明,垫底势力的形式对静摩擦力的大小有很重要的影响.     

Quantum Cherenkov radiation at the motion of a small neutral particle parallel to the surface of a transparent dielectric

Quantum Cherenkov radiation and quantum friction at the motion of a small neutral particle parallel to the surface of a transparent dielectric with the refractive index n have been studied in a fully relativistic theory. Radiation appears at velocities above the threshold value, v > v _c = c/n. The friction force in the particle–plate configuration has been derived from the friction force in the plate–plate configuration under the assumption that one of the plates is significantly decharged. A decrease in the kinetic energy of the particle near the threshold velocity is due to its radiation and near the speed of light is determined by the heat power absorbed by the particle in the rest frame. The powers of quantum and classical Cherenkov radiation can be comparable in the relativistic case.     

Frenkel-Kontorova模型中垫底势对最大静摩擦力的影响

用一维Frenkel-Kontorova模型,对相互接触的两个单原子分子链具有相对运动趋势时所产生的最大静摩擦力进行了研究.分别在相邻原子的距离与周期势场的周期比b/a为可公度(commensurate)、黄金分割(golden mean)、螺旋分割(spiral mean)三种情况下,描述了特殊垫底势力的振幅A与分子链静摩擦力的关系,在特殊垫底势力的作用下上层原子链弹性系数K对静摩擦力的影响.研究表明,垫底势力的形式对静摩擦力的大小有很重要的影响. 关键词： Frenkel-Kontorova模型 静摩擦力     

Surface anisotropy of CrxN1−x films prepared on an inner wall by magnetic sputtering

The Cr_xN_1−x films were prepared by magnetic sputtering on an inner wall of a column. Their surface morphologies were studied by atomic force microscopy (AFM) and found to be anisotropic. The 3-D AFM images indicate the grains grow upward along the rotational axis of the system. The AFM top views show a mosaic-like pattern for all samples. Analysis of the height-height correlation function demonstrates that correlation length along the rotational axis of the system is longer than that vertical to the axis. The correlation length and RMS roughness increase with the flow rate of N₂. A deposition model proposed that the shadowing effect of the reactive gas N₂ is the dominant factor for surface anisotropy. The bias added on the substrate is regarded to modulate the grain direction to the rotation axis and enhance roughness and defects.     

Modelling of a two-dimensional Coulomb friction oscillator

Xia proposes a model for investigating the stick-slip motion caused by dry friction of a two-dimensional oscillator under arbitrary excitations. Instead of the harmonic balance method used by most investigators, a numerical approach to investigate the system is provided. The concept of the friction direction angle is introduced to determine the components of the static and kinetic friction force vector and the hyperbolic secant function is introduced to deal with the transition of the friction force from the static to the kinetic state. The friction direction angle is determined by either relative velocities or input forces. With this method the switch conditions for stick state, slip state and stick-slip state can be easily derived. The orbits of the responses, which are either straight line segments, circular or elliptic are obtained. In the general case, the orbit of the response is a complex planar curve. Zero-stop, one-stop, two-stops and more than two-stops per cycle are also found.     

Frenkel-Kontorova模型中基底势振动的影响

基于一维Frenkel-Kontorova模型, 研究了振动的基底势对系统纳米摩擦现象的影响. 分别在相邻原子间的距离与周期势场的周期比为不公度(incommensurate)、可公度(commensurate)两种情形下, 探讨了基底势振动的振幅和频率对滞回现象(hysteresis)、最大静摩擦力以及超滑现象的作用机理. 两种情形下, 固定频率, 随着振幅的增大, 滞回区域的面积以及最大静摩擦力都将减小, 对于不同的频率, 减小的趋势不同. 系统甚至产生了超滑现象. 但当频率过大时, 振幅的改变不会影响滞回区域的面积以及最大静摩擦力的大小, 此时与基底不加振动时的情形一致; 当振幅固定, 随着频率的增大, 滞回区域的面积将增大, 对于不同振幅, 增大的趋势不同. 特别地, 对于某些固定的振幅, 最大静摩擦力随着振动频率的增大先逐步减小直至出现超滑现象, 再进一步增大频率, 最大静摩擦力又转而逐步增大. 这一现象类似于共振, 表明存在最佳的振动频率促进系统内所有原子的共同运动, 使得整个系统的最大静摩擦力几乎消失. 另外, 两种情形的区别是, 对于某些固定的频率(如ω= 0.5)和不同的小振幅, 不可公度情形往往具有相同的平均终止速度, 而可公度情形则不同, 表明相同前提下后者具有更复杂的动力学行为. 关键词： Frenkel-Kontorova模型 滞回 最大静摩擦力 超润滑     

Dry friction in the Frenkel-Kontorova-Tomlinson model: dynamical properties

Wearless friction is investigated in a simple mechanical model called Frenkel-Kontorova-Tomlinson model. We have introduced this model in [Phys. Rev. B, 53, 7539 (1996)] where the static friction has already been considered. Here the model is treated for constant sliding speed. The motion of the internal degrees of freedom is regular for small sliding velocities or weak interaction between the sliding surfaces. The regular motion for large velocities is strongly determined by normal and superharmonic resonance of phonons excited by the so-called “washboard wave”. The kinetic friction has maxima near these resonances. For increasing interaction strength the regular motion becomes unstable due to parametric resonance leading to quasistatic and chaotic motion. For sliding velocities beyond first-order parametric resonance bistability occurs between the strongly chaotic motion (fluid sliding state), where friction is large and a regular motion (solid sliding state), where friction is weak. The fluid sliding state is mainly determined by the density of decay channels of m washboard waves into n phonons. This density describes qualitatively the effectiveness of the energy transfer from the uniform sliding motion into the microscopic, irregular motion of the degrees of freedom at the sliding interface. For a narrow interval of the sliding velocities we also found enhanced friction due to coherent motion. In the regime of coherent motion nondestructive interactions of dark envelope solitons occur.     

Drift velocity in the necklace model for reptation in a two-dimensional square lattice

We report the chain dynamics in the necklace model that mimics the reptation of a chain of N particles in a two-dimensional square lattice. We focus on the drift velocity under an applied static field. The characteristics of the model allow us to determine the effects of the forces on the chains and the resulting mechanisms that affect the drift velocity. Results obtained through Monte Carlo simulations were analyzed and discussed and distinct regimes as a function of the force strength and N were identified. We found that for small total applied forces, the drift velocity scales as 1/N. When the applied force to every particle is small but the total applied force is not, the tube deforms in such a way that the drift velocity does not depend on N. Large forces, applied to every particle, can straight chains such that the distance between the chain ends increases faster than the number of particles. Also, large forces can deform the chain within the tube what is directly related to a decrease of the drift velocity.     

Dynamique des surfaces inhomogènes

We investigate the influence of inhomogeneous layers at the surface of a crystal on its elastic properties. This problem occurs when several layers of different materials are deposited on a substrate, but also during special treatments of solids like quenching or cold-working. We model the presence of inhomogeneities by N adlayers with different parameters. We assume that the solids are all of hexagonal symmetry (the isotropic materials being a particular case) and the interfaces between the media are (0001). By assuming that the total width h of the adlayers is small compared to the wavelength, we show that the presence of these layers is equivalent to effective boundary conditions at the surface of the substrate, which we derive to the first order in h. These equations depend on the parameters of the adlayers through some particular averages. We can then generalize to inhomogeneous surfaces the results we derived previously for the influence of only one adlayer on different elastic properties of the substrate.     

Theoretical analysis of optical properties of dielectric coatings dependence on substrate subsurface defects

A model for refractive index of stratified dielectric substrate was put forward according to theories of inhomogeneous coatings. The substrate was divided into surface layer, subsurface layer and bulk layer along the normal direction of its surface. Both the surface layer (separated into N₁ sublayers of uniform thickness) and subsurface layer (separated into N₂ sublayers of uniform thickness), whose refractive indices have different statistical distributions, are equivalent to inhomogeneous coatings, respectively. And theoretical deduction was carried out by employing characteristic matrix method of optical coatings. An example of mathematical calculation for optical properties of dielectric coatings had been presented. The computing results indicate that substrate subsurface defects can bring about additional bulk scattering and change propagation characteristic in thin film and substrate. Therefore, reflectance, reflective phase shift and phase difference of an assembly of coatings and substrate deviate from ideal conditions. The model will provide some beneficial theory directions for improving optical properties of dielectric coatings via substrate surface modification.     

Mapping charge-mosaic surfaces in electrolyte solutions using surface charge microscopy

A significant limitation of electrokinetic measurements is that only an average value of the zeta potential/streaming potential is measured—regardless of whether the surface charge distribution is homogeneous or otherwise. However, in real-world situations, nearly all solids (and liquids) of technological significance exhibit surface heterogeneities. To detect heterogeneities in surface charge, analytical tools which provide accurate and spatially resolved information about material surface potential—particularly at microscopic and sub-microscopic resolutions—are needed.A novel AFM-based technique for mapping surface charge domains on heterogeneous surfaces, which we call Surface Charge Microscopy (SCM), was recently introduced by our research team. It relies on recording colloidal force curves over multiple locations on the substrate surface using small probes. The surface charge characteristics of the heterogeneous substrate are determined from the recorded colloidal force curves, allowing for the surface charge variation to be mapped. In this communication, we briefly review the SCM technique. Examples of results of measurements of the surface interaction forces that were recorded between a silicon nitride AFM cantilever and a multi-phase volcanic rock and heterogeneous surface of bitumen are also given.     

One-body nuclear friction

We have calculated the velocity dependent forces acting between two nuclei that arise due to one-body mechanism of nuclear excitation when they are dragged against one another with constant velocity. The nuclear friction coefficients are then extracted from the velocity dependence of these forces which is found to be strongly linear. The one-body force is calculated by solving the time-dependent Schrödinger equation for all the occupied single-particle states of a nuclear system in a central collision. Each nucleus in this model is assumed to be described by a single-particle Woods-Saxon potential filled with 40 nucleons each. The magnitude of the resulting one-body friction is found to be in between the proximity and surface frictions. The proximity-friction is too small by about an order of magnitude. To check this result, we calculated the one-sided flux from one nucleus to the other. The friction force connected to this flux (i.e. the one-body exchange friction) turns out to be about half or less than the one body friction. We conclude that theproximity-friction grossly underestimates the one-body exchange friction. Furthermore,inelastic excitations are at least as important for one-body dissipation at distances beyond the touching point as is particle exchange.     

Friction behavior of monolayer molybdenum diselenide nanosheet under normal electric field

The friction behavior of monolayer molybdenum diselenide (MoSe₂) under normal electric field was studied by the atomic force microscope. The friction coefficients of MoSe₂ are increasing with bias voltage applied on the Si substrate. The results show that the adhesion and electrostatic forces increase with bias and approximately follow a parabolic law. The friction force and surface potential are of the same tendency with bias application time, and the contribution of charges accumulation to friction is considerable. The mechanisms of the friction behavior under external normal electric field were explained with electrostatic force and adsorption. This study reveals a possibility of electronically controlling friction in two-dimensional MoSe₂ system, with potential applications in solid lubricant and moving parts for MEMS devices.     

Friction and normal forces of model friction modifier additives in simulations of boundary lubrication

ABSTRACT

Interaction forces between solid surfaces are often mitigated by adsorbed molecules that control normal and friction forces at nanoscale separations. Molecular dynamics simulations were conducted of opposing semi-ordered monolayers of united-atom chains on sliding surfaces to relate friction and normal forces to imposed sliding velocity and inter-surface separation. Practical examples include adsorbed friction-modifier molecules in automatic transmission fluids. Friction scenarios in the simulations had zero, one, or two fluid layers trapped between adsorbed monolayers. Sliding friction forces increased with sliding velocity at each stable separation. Lower normal forces were obtained than in most previous nanotribology molecular simulations and were relatively independent of sliding speed. Distinguishing average frictional force from its fluctuations showed the importance of system size. Uniform velocities were obtained in the sliding direction across each adsorbed film, with a gradient across the gap containing trapped fluid. The calculated friction stress was consistent with measurements reported using a surface forces apparatus, indicating that drag between an adsorbed layer and trapped fluid can account sufficiently for sliding friction in friction modifier systems. An example is shown in which changes in molecular organisation parallel to the surface led to a large change in normal force but no change in friction force.     

Fokker–Planck Equation,Molecular Friction,and Molecular Dynamics for Brownian Particle Transport near External Solid Surfaces

The Fokker–Planck (FP) equation describing the dynamics of a single Brownian particle near a fixed external surface is derived using the multiple-time-scales perturbation method, previously used by Cukier and Deutch and Nienhuis in the absence of any external surfaces, and Piasecki et al. for two Brownian spheres in a hard fluid. The FP equation includes an explicit expression for the (time-independent) particle friction tensor in terms of the force autocorrelation function and equilibrium average force on the particle by the surrounding fluid and in the presence of a fixed external surface, such as an adsorbate. The scaling and perturbation analysis given here also shows that the force autocorrelation function must decay rapidly on the zeroth-order time scale ₀, which physically requires N _Kn1, where N _Kn is the Knudsen number (ratio of the length scale for fluid intermolecular interactions to the Brownian particle length scale). This restricts the theory given here to liquid systems where N _Kn1. For a specified particle configuration with respect to the external surface, equilibrium canonical molecular dynamics (MD) calculations are conducted, as shown here, in order to obtain numerical values of the friction tensor from the force autocorrelation expression. Molecular dynamics computations of the friction tensor for a single spherical particle in the absence of a fixed external surface are shown to recover Stokes' law for various types of fluid molecule–particle interaction potentials. Analytical studies of the static force correlation function also demonstrate the remarkable principle of force-time parity whereby the particle friction coefficient is nearly independent of the fluid molecule–particle interaction potential. Molecular dynamics computations of the friction tensor for a single spherical particle near a fixed external spherical surface (adsorbate) demonstrate a breakdown in continuum hydrodynamic results at close particle–surface separation distances on the order of several molecular diameters.     

Comparison of surface films formed on titanium by pulsed Nd:YAG laser irradiation at different powers and wavelengths in nitrogen atmosphere

The nitridation of titanium (Ti) caused by a Q-switched Nd:YAG laser under nitrogen gas atmosphere was investigated in situ using X-ray photoelectron spectroscopy (XPS). A laser having a wavelength of 1064 nm and 532 nm (SHG mode) was irradiated on a titanium substrate in an atmosphere-controlled chamber, and the substrate was then transported to an XPS analysis chamber without exposing it to air. The characteristics of the surface layer strongly depend on the laser power. When the power is relatively low, a titanium dioxide layer containing a small amount of nitrogen is formed on the substrate. Laser irradiation beyond a certain laser power is required to obtain a stoichiometric titanium nitride (TiN) layer. A TiN layer and an oxynitride layer with a TiO_xN_y-like structure are formed as the topmost and the lower surface layer, respectively, when the laser power exceeds this threshold value. The threshold laser power strongly depends on the wavelength of the laser, and this threshold value for the 532-nm laser is quite lower than that for the 1064-nm laser.     

Tribological Behavior of Multiply-Alkylated Cyclopentanes (MACs)-Cu Nanoparticles Composite Thin Film

Multiply-alkylated cyclopentanes (MACs) composite thin films containing Cu nanoparticles are fabricated on the octadecyltrichlorosilane (OTS)-modified substrate by a spin-coating technique. The thickness, wetting behavior, and nanoscale morphologies of the films are characterized by means of ellipsometry, contact angle measurement, and atomic force microscope (AFM). The friction and wear behaviors of the thin films sliding against Si₃N₄ ball are examined on a UMT-2MT tribometer in a ball-on-disk contact mode. The worn surfaces of the OTS-MAC-Cu composite film and the counterpart Si₃N₄ balls are investigated with a scanning electron microscope. Water contact angle on OTS-MAC-Cu composite film is higher than that of OTS-MAC film. OTS-MAC-Cu composite film exhibits higher load-carrying capacity and better friction reduction and antiwear behavior as compared with OTS-MAC film. This may be attributed to the load-carrying and self-repairing property of the Cu nanoparticles in the composite film and the formation of a transfer layer composed of OTS, MAC, and Cu on the rubbing surface of the counterpart ball.     

Stochastic rolling of a rigid sphere in weak adhesive contact with a soft substrate

We study the rolling motion of a small solid sphere on a fibrillated rubber substrate in an external field in the presence of a Gaussian noise. From the nature of the drift and the evolution of the displacement fluctuation of the ball, it is evident that the rolling is controlled by a complex non-linear friction at a low velocity and a low noise strength (K), but by a linear kinematic friction at a high velocity and a high noise strength. This transition from a non-linear to a linear friction control of motion can be discerned from another experiment in which the ball is subjected to a periodic asymmetric vibration in conjunction with a random noise. Here, as opposed to that of a fixed external force, the rolling velocity decreases with the strength of the noise suggesting a progressive fluidization of the interface. A state (K) and rate (V) dependent friction model is able to explain both the evolution of the displacement fluctuation as well as the sigmoidal variation of the drift velocity with K. This research sets the stage for studying friction in a new way, in which it is submitted to a noise and then its dynamic response is studied using the tools of statistical mechanics. Although more works would be needed for a fuller realization of the above-stated goal, this approach has the potential to complement direct measurements of friction over several decades of velocities and other state variables. It is striking that the non-Gaussian displacement statistics as observed with the stochastic rolling is similar to that of a colloidal particle undergoing Brownian motion in contact with a soft microtubule.     

Fabrication and wear protection performance of superhydrophobic surface on zinc

A simple two-step process has been developed to render zinc surface superhydrophobic, resulting in low friction coefficient and long wear resistance performance. The ZnO film with uniform and packed nanorod structure was firstly created by immersing the zinc substrates into 4% N,N-dimethylformamide solution. The as-fabricated surface was then coated a layer of fluoroalkylsilane (FAS) by gas phase deposition. Scanning electron microscopy (SEM) and water contact angle (WCA) measurement have been performed to characterize the morphological feature, chemical composition and superhydrophobicity of the surface. The resulting surfaces have a WCA as high as 156° and provide effective friction-reducing and wear protection for zinc substrate.     

Effects of substrate bias and nitrogen flow ratio on the surface morphology and binding state of reactively sputtered ZrNx films before and after annealing

ZrN_x films were sputtered in an Ar + N₂ atmosphere, with different substrate biases (0 to −200 V) at various nitrogen flow ratios (%N₂ = 0.5-24%). The surface morphology, resistivity, crystllinity, and bonding configuration of ZrN_x films, before and after vacuum annealing, were investigated. As compared with ZrN_x films grown without substrate bias, before and after annealing, the resistivity of 1% and 2% N₂ films decreases with increasing substrate biases. Simultaneously, if the applied bias is too high, the crystallinity of ZrN_x film will decrease. The surfaces of 1% and 2% N₂ flow films deposited without bias have small nodules, whereas the surface morphology of films deposited at −100 V of substrate bias exhibits large nodules and rugged surface. Once a −200 V of substrate bias is applied to the substrate, the surface morphology of ZrN_x films, grown at 1% and 2% nitrogen flow ratios, is smooth. Furthermore, there are two deconvoluted peaks in XPS spectra (i.e., Zr-O and Zr-N) of ZrN_x films deposited at −200 V of substrate bias before and after annealing. On the other hand, the surface morphology changes dramatically from rugged surfaces for film deposited at lower nitrogen flow ratio (%N₂ < 1%) to smoother and denser surfaces for film grown at higher nitrogen flow ratio (%N₂ ≥ 1%). The Zr-N bonding in 2% N₂ films still exist after annealing at 700 °C, while the Zr-N bonding in 0.5% and 16% N₂ flow film vanish at the same temperature. The connection between the resistivity, crystallinity, surface morphology, and bonding configuration of ZrN_x films and how they are influenced by the substrate bias and nitrogen flow ratio are discussed in this paper.