Noncontact friction and relaxational dynamics of surface defects

The motion of a cantilever near sample surfaces exhibits additional friction even before two bodies come into mechanical contact. Called noncontact friction (NCF), this friction is of great practical importance to the ultrasensitive force detection measurements. The observed large NCF of a micron-scale cantilever found an anomalously large damping that exceeds theoretical predictions by 8-11 orders of magnitude. This finding points to a contribution beyond fluctuating electromagnetic fields within the van der Waals approach. Recent experiments reported by Saitoh et al. [Phys. Rev. Lett. 105, 236103 (2010)] also found a nontrivial distance dependence of NCF. Motivated by these observations, we propose a mechanism based on the coupling of a cantilever to the relaxation dynamics of surface defects. We assume that the surface defects couple to the cantilever tip via spin-spin coupling and their spin relaxation dynamics gives rise to the backaction terms and modifies both the friction coefficient and the spring constant. We explain the magnitude, as well as the distance dependence of the friction due to these backaction terms. Reasonable agreement is found with the experiments.     

缺陷对碳纳米管摩擦与运动行为的影响

本文采用分子动力学方法研究了公度、无公度情况下含空位、Stone-Thrower-Wales(STW)型缺陷的单壁碳纳米管(SWCNT)在石墨基底上的摩擦与运动行为.结果表明,公度时缺陷的存在导致了界面局部无公度,减小了摩擦.随着碳纳米管底部STW缺陷的增多,碳纳米管变形增大,侧向力波动的幅值减小,局部无公度性增强,摩擦减小.含空位缺陷的碳纳米管所受的摩擦力明显大于含STW缺陷的碳纳米管,原因在于含空位缺陷的碳纳米管在运动的后期出现了明显的翻转现象,增大了能量耗散.无公度时,碳纳米管与石墨基底间的摩擦力很小,缺陷对其摩擦力影响不大,原因在于无论是否含有缺陷,碳纳米管与石墨组成的界面的无公度性差别不大.     

摩擦微观能量耗散机理的复合振子模型研究

提出无磨损界面摩擦微观能量耗散机理的复合振子模型，指出滑动摩擦过程同时存在整体做低频弹性振动的宏观振子和界面原子受激励产生热振动的微观振子，并在此基础上分析了宏观振子和微观振子对摩擦能量耗散的不同影响. 通过对界面原子的动力学分析，指出摩擦过程界面激励力的频率是能量转换的关键:在平衡力作用阶段，界面作用力的频率趋于零，因而可以直接作用到每个原子，力的作用效果是整体和均匀的；在失稳跳跃阶段,由于界面激励力的频率极高，造成摩擦界面原子获得的能量分布很不均匀，从而产生不可逆的能量耗散过程. 与目前通用的独立振子模型比较，复合振子模型能够更准确描述摩擦能量耗散过程，可为摩擦控制提供理论指导. 关键词： 摩擦 能量耗散机理 复合振子模型 独立振子模型     

Computer simulation of amplitude-dependent internal friction

The internal friction in crystalline materials has been studied in the model of viscous motion of dislocations through a system of randomly arranged defects. The results of the calculation of the amplitude dependence of the internal friction for different frequencies and defects of different powers are presented. Three characteristic portions have been revealed in the amplitude dependences of the internal friction, which correspond to different modes of dislocation motion.     

Atomic friction

We show that wearless atomic friction, recently observed by AFM techniques, is well desribed by the mechanism of “plucking of atoms” proposed by Tomlinson in 1929. Our results for a single-asperity contact yield a satisfactory fit of the experimental data. For extended contact areas, the relative orientation of the crystal lattices and the resulting misfit becomes important. The misfit gives rise to the formation of domains where the two surface structures are approximately in registry. The domains are separated by two sets of shift lines, crossing each other in topological defects. During quasistatic sliding, the whole domain pattern moves perpendicular to the driving force. Frictional behaviour occurs if the ratio of the coupling strength of the surface atoms to the bulk of the body to the potential barrier for sliding is less than a critical value. Dissipation and friction hysteresis are caused by irreversible jumps of these topological defects. The friction force depends strongly on both the sliding direction and the misfit angle.     

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.     

Energy dissipation in solid friction

Dissipation in solid friction is studied as a function of the elastic properties of the two sliding surfaces. The two surfaces have been constructed by embedding macroscopic asperities in an elastic layer. It is shown that when the surfaces are rigid the energy dissipation is smaller than in the elastic case. The scaling of the friction force as a function of the asperity number is also studied. Received 9 November 1998     

Macroscopic approach to the Casimir friction force

The general formula is derived for the vacuum friction force between two parallel perfectly flat planes bounding two material media separated by a vacuum gap and moving relative to each other with a constant velocity v. The material media are described in the framework of macroscopic electrodynamics whereas the nonzero temperature and dissipation are taken into account by making use of the Kubo formulas from non-equilibrium statistical thermodynamics. The formula obtained provides a rigorous basis for calculation of the vacuum friction force within the quantum field theory methods in the condensed matter physics. The revealed v dependence of the vacuum friction force proves to be the following: for zero temperature (T = 0) it is proportional to (v/c)³ and for T > 0 this force is linear in v/c.     

Static friction between elastic solids due to random asperities

Several workers have established that the Larkin domains for two three-dimensional nonmetallic elastic solids in contact with each other at a disordered but atomically flat interface are enormously large, implying that there should be negligible static friction per unit area in the macroscopic solid limit. In contrast, the present Letter argues that when the Larkin domains are calculated for disorder on the multiasperity scale, they are much smaller than the interface size. This can account for the virtual universal occurrence of static friction.     

Viscous friction in foams and concentrated emulsions under steady shear

We present a model for the viscous friction in foams and concentrated emulsions, subject to steady shear flow. First, we calculate the energy dissipated due to viscous friction inside the films between two neighboring bubbles or drops, which slide along each other in the flow. Next, from this energy we calculate the macroscopic viscous stress of the sheared foam or emulsion. The model predictions agree well with experimental results obtained with foams and emulsions.     

Texture-induced modulations of friction force: the fingerprint effect

Modulations of the friction force in dry solid friction are usually attributed to macroscopic stick-slip instabilities. Here we show that a distinct, quasistatic mechanism can also lead to nearly periodic force oscillations during sliding contact between an elastomer patterned with parallel grooves, and abraded glass slides. The dominant oscillation frequency is set by the ratio between the sliding velocity and the grooves period. A model is derived which quantitatively captures the dependence of the force modulations amplitude with the normal load, the grooves period, and the slides roughness characteristics. The model's main ingredient is the nonlinearity of the friction law. Since such nonlinearity is ubiquitous for soft solids, this "fingerprint effect" should be relevant to a large class of frictional configurations and have important consequences in human digital touch.     

Molecular-dynamics simulations with explicit hydrodynamics I: On the friction coefficients of deformed polymers

We implement large-scale Molecular-Dynamics (MD) simulations which incorporate hydrodynamic interactions via the inclusion of explicit Lennard-Jones solvent to examine the behaviour of polymer chains in sieving media. We begin by examining the friction coefficients of polymers in long-lived states responsible for inducing length-dependent mobility, i.e., allowing separation of polymers (or polyelectrolytes) by molecular weight. In particular, the conformations we examine occur in devices which utilize arrays of molecular obstacles or dilute solutions of polymers. We compare the results from our MD simulations with expressions from macroscopic hydrodynamics for four specific cases: i) a random coil excluded-volume Zimm polymer, ii) a rigid polymer moving perpendicular to its major axis iii) a rigid polymer moving parallel to its major axis and iv) a rigid polymer, folded at different points along its contour. We also examine the behaviour of the friction coefficient of a fully flexible molecule pulled by its middle monomer as a function of an applied force F and show that there are several distinct frictional regimes.PACS: 83.10.Mj Molecular dynamics, Brownian dynamics - 61.41. + e Polymers, elastomers, and plastics - 82.20.Wt Computational modeling; simulation     

Dislocation-induced internal friction of a material with vacancies in weak magnetic field pulses

It is found that the form of the amplitude dependence of low-frequency internal friction in a quenched and aged aluminum sample (99.999% pure) changes under the effect of weak magnetic field pulses (H≥10⁵ A/m): the general level of internal friction increases. This effect is attributed to the influence of a magnetic field on the structural complex formed by a dislocation and point defects (the role of point defects is played by vacancies).     

Calculations of temperature conditions in a contact spot of friction with seizure

Temperature conditions in a contact spot of friction with seizure are investigated using a macroscopic self-oscillation model. Both the flash temperature at the friction surface and the thickness of the surface material layer, where the temperature oscillates, are estimated at different loads, sliding velocities, and friction coefficients. The influence of the contact spot size on the flash temperature is studied. The calculated results for steel and copper samples are compared. Institute of Strength Physics and Materials Science. Translated from Izvestiya Vyshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 58–64, September 1999.     

Solute friction and forest interaction

Solute friction is known to prevail in crystals where a solution of point defects results in a diffuse resistance to dislocation motion. This property is often used to strengthen materials. In this paper we show that it also affects dislocation–dislocation interactions. Dislocation dynamics simulations are used to investigate and quantify this property. The solute friction results in a shielding of elastic interactions leading to a significant decrease of the intrinsic strengths of junction and annihilation reactions. Simulations in static and dynamic conditions show that the interaction stability decreases with the friction stress. A model is proposed to account for the modification of the interaction coefficient predicted by massive simulations in latent hardening conditions. Results suggest that the observed softening is mainly due to the decrease of the line tension of dislocations involved in the dislocation–dislocation interactions.     

Transition from static to kinetic friction: insights from a 2D model

We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic-slider-rigid-substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory microslip fronts are successfully reproduced. From the analysis of the interfacial stresses, we derive a prediction for the evolution of the precursor length as a function of the applied loads, as well as an approximate relationship between microscopic and macroscopic friction coefficients. We show that the stress buildup due to both elastic loading and microslip-related relaxations depends only weakly on the underlying shear crack propagation dynamics. Conversely, crack speed depends strongly on both the instantaneous stresses and the friction coefficients, through a nontrivial scaling parameter.     

Giant enhancement of noncontact friction between closely spaced bodies by dielectric films and two-dimensional systems

The effect of an external bias voltage and spatial variations of the surface potential on the damping of cantilever vibrations in an atomic force microscope (AFM) is considered. The damping is due to an electrostatic friction that arises due to dissipation of the energy of an electromagnetic field generated in the sample by oscillating static charges induced on the surface of the AFM probe tip by the bias voltage or spatial variations of the surface potential. A similar effect appears when the tip is oscillating in an electrostatic field created by charged defects present in the dielectric sample. The electrostatic friction is compared to the van der Waals (vdW) friction between closely spaced bodies, which is caused by a fluctuating electromagnetic field related to the quantum and thermal fluctuations of current density inside the bodies. It is shown that the electrostatic friction and the vdW friction can be strongly enhanced in the presence of dielectric films or two-dimensional (2D) structures—such as a 2D electron system or an incommensurate layer of adsorbed ions exhibiting acoustic oscillations—on the probe tip and sample surfaces. It is also shown that the damping of cantilever oscillations caused by the electrostatic friction in the presence of such 2D structures can have the same order of magnitude and the same dependence on the distance as observed in experiment by Stipe et al. [Phys. Rev. Lett. 87, 096801 (2001)]. At small distances, the vdW friction can be large enough to be measured in experiment. In interpreting the experimental data that obey a quadratic dependence on the bias voltage, one can reject a phonon mechanism according to which the friction depends on the fourth power of the voltage.     

Casimir friction force between polarizable media

This work is a continuation of our recent series of papers on Casimir friction, for a pair of particles of low relative particle velocity. Each particle is modeled as a simple harmonic oscillator. Our basic method, as before, is the use of quantum mechanical statistical mechanics, involving the Kubo formula, at finite temperature. In this work we begin by analyzing the Casimir friction between two particles polarizable in all spatial directions, this being a generalization of our study in [J.S. Høye, I. Brevik, Europhys. Lett. 91, 60003 (2010)], which was restricted to a pair of particles with longitudinal polarization only. For simplicity the particles are taken to interact via the electrostatic dipole-dipole interaction. Thereafter, we consider the Casimir friction between one particle and a dielectric half-space, and also the friction between two dielectric half-spaces. Finally, we consider general polarizabilities (beyond the simple one-oscillator form), and show how friction occurs at finite temperature when finite frequency regions of the imaginary parts of polarizabilities overlap.