scholarly journals Statistics of Sliding on Periodic and Atomically Flat Surfaces

2021 ◽  
Vol 7 ◽  
Author(s):  
Maja Srbulovic ◽  
Konstantinos Gkagkas ◽  
Carsten Gachot ◽  
András Vernes
Keyword(s):  
Equations Of Motion ◽  
Two Dimensions ◽  
Analytical Models ◽  
Fourier Series Expansion ◽  
Stick Slip ◽  
Time Resolved ◽  
Flat Surfaces ◽  
Atomic Force ◽  
Reaction Forces ◽  
Atomically Flat

Among the so-called analytical models of friction, the most popular and widely used one, the Prandtl-Tomlinson model in one and two dimensions is considered here to numerically describe the sliding of the tip within an atomic force microscope over a periodic and atomically flat surface. Because in these PT-models, the Newtonian equations of motion for the AFM-tip are Langevin-type coupled stochastic differential equations the resulting friction and reaction forces must be statistically correctly determined and interpreted. For this, it is firstly shown that the friction and reaction forces as averages of the time-resolved ones over the sliding part, are normally (Gaussian) distributed. Then based on this, an efficient numerical scheme is developed and implemented to accurately estimate the means and standard deviations of friction and reaction forces without performing too many repetitions for the same sliding experiments. The used corrugation potential is the simplest one obtained from the Fourier series expansion of the two-dimensional (2D) periodic potential, e.g., for an fcc(111) surface, which permits sliding on both commensurate and incommensurate paths. In this manner, it is proven that the PT-models predict both frictional regimes, namely the structural superlubricity and stick-slip along (in)commensurate sliding paths, if the ratio of mean corrugation and elastic energies is properly set.

Use of the Atomic Force Microscope to Study Mechanical Properties of Lubricant Layers

MRS Bulletin ◽  
1993 ◽  
Vol 18 (5) ◽  
pp. 20-25 ◽  
Author(s):  
Miquel B. Salmeron
Keyword(s):  
Atomic Force Microscope ◽  
Surface Force ◽  
Separation Distance ◽  
Atomic Scale ◽  
Simple Estimate ◽  
Flat Surfaces ◽  
Atomic Force ◽  
Length Increase ◽  
Order Of Magnitude ◽  
Atomically Flat

Advances in our understanding of the phenomena of adhesion, friction, and lubrication are facilitated by the recent development of new tools that allow the study of contacts in close-to-ideal conditions. These new tools are the surface force spparatus (SFA) and the atomic force microscope (AFM). The first was developed by Israelachvili in the 1970s. In this device, contact between two atomically flat surfaces of mica occurs over an area of several micrometers in diameter after the mica sheets, glued onto two perpendicular cylindrical lenses, are compressed. Force, area of contact, and separation distance can be controlled at the atomic scale. The second device, the AFM, was developed by Binnig et al. in 1986. The sharp tip of the AFM is a convenient idealization of a single asperity. In addition, the AFM can be used to image the surface in the weak repulsive or in the attractive modes so that minimum perturbation is introduced by the imaging process itself. These two devices have the necessary sensitivity to allow the application of forces weak enough not to dislodge atoms from their sites during contact. The order of magnitude of the force that can lead to the rupture of chemical bonds is a convenient figure to keep in mind in this context. A simple estimate of this force is obtained by considering a bond-length increase of 1 Å as leading to dissociation. For a bond energy of ≈1 eV, Fb ≈ 1 eV/1 Å ≈ 1 × 10−9 N.

Self-Organized Criticality in Nanotribology

2003 ◽  
Vol 782 ◽  
Author(s):  
Micha Adler ◽  
John Ferrante ◽  
Alan Schilowitz ◽  
Dalia Yablon ◽  
Fredy Zypman
Keyword(s):  
Dry Friction ◽  
Sliding Friction ◽  
Stick Slip ◽  
Slip Mechanism ◽  
Flat Surfaces ◽  
Self Organized ◽  
Atomic Force ◽  
Lateral Forces ◽  
Self Organized Criticality ◽  
Sliding Distance

ABSTRACTWe present experimental results on dry friction, which are consistent with the hypothesis that the stick-slip mechanism for energy release is described by self-organized criticality. The data, obtained with an Atomic Force Microscope set to measure lateral forces– examines the variation of the friction force as a function of time – or sliding distance. The materials studied were nominally flat surfaces of mica, quartz, silica and steel. An analysis of the data shows that the probability distribution of slip sizes follows a power law. Our data strongly supports the existence of self-organized criticality for nano-stick-slip in dry sliding friction.

scholarly journals PHASE DYNAMICS AND KINETICS OF THIN LUBRICANT FILM DRIVEN BY CORRELATED TEMPERATURE FLUCTUATIONS

2007 ◽  
Vol 07 (02) ◽  
pp. L111-L133 ◽  
Author(s):  
ALEXEI V. KHOMENKO ◽  
IAKOV A. LYASHENKO
Keyword(s):  
Sliding Friction ◽  
Temperature Fluctuations ◽  
Lubricant Film ◽  
Stick Slip ◽  
Flat Surfaces ◽  
Phase Dynamics ◽  
Damped Oscillations ◽  
Atomically Flat ◽  
Kinetics Of ◽  
Stable Sliding

The melting of an ultrathin lubricant film is studied at friction between atomically flat surfaces. We take into account fluctuations of lubricant temperature, which are defined by the Ornstein-Uhlenbeck process. Phase diagrams and portraits are calculated for second- and first-order transitions (the melting of an amorphous and that of a crystalline lubricants, respectively). It is shown that, in the former case, a stick-slip friction domain, separating the regions of dry and sliding friction, appears. In the latter case, three domains of stick-slip friction arise, which are characterized by the transitions between dry, metastable and stable sliding friction. The increase in the correlation time of lubricant temperature fluctuations leads to increasing in the rubbing-surface temperature needed for realization of sliding friction. The stationary states, corresponding to dry, stable and metastable sliding friction, are reached as a result of damped oscillations.

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

Quasi-Barrierless Submolecular Motion in Mechanically Interlocked Carbon Nanotubes

2020 ◽  
Author(s):  
Julia Villalva ◽  
Belén Nieto-Ortega ◽  
Manuel Melle-Franco ◽  
Emilio Pérez
Keyword(s):  
Density Functional ◽  
Close Contact ◽  
Tight Binding ◽  
Energetic Cost ◽  
Molecular Fragments ◽  
Activation Barriers ◽  
Flat Surfaces ◽  
Different Types ◽  
Atomically Flat ◽  
Derivatives Of

The motion of molecular fragments in close contact with atomically flat surfaces is still not fully understood. Does a more favourable interaction imply a larger barrier towards motion even if there are no obvious minima? Here, we use mechanically interlocked rotaxane-type derivatives of SWNTs (MINTs) featuring four different types of macrocycles with significantly different affinities for the SWNT thread as models to study this problem. Using molecular dynamics, we find that there is no direct correlation between the interaction energy of the macrocycle with the SWNT and its ability to move along or around it. Density functional tight-binding calculations reveal small (<2.5 Kcal·mol-1) activation barriers, the height of which correlates with the commensurability of the aromatic moieties in the macrocycle with the SWNT. Our results show that macrocycles in MINTs rotate and translate freely around and along SWNTs at room temperature, with an energetic cost lower than the rotation around the C−C bond in ethane.<br>

scholarly journals Horizon radiation reaction forces

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Walter D. Goldberger ◽  
Ira Z. Rothstein
Keyword(s):  
Black Hole ◽  
Equations Of Motion ◽  
Finite Size ◽  
Radiation Reaction ◽  
Effective Field ◽  
Compact Objects ◽  
Finite Size Effect ◽  
Binary Black Holes ◽  
Dissipative Effects ◽  
Reaction Forces

Abstract Using Effective Field Theory (EFT) methods, we compute the effects of horizon dissipation on the gravitational interactions of relativistic binary black hole systems. We assume that the dynamics is perturbative, i.e it admits an expansion in powers of Newton’s constant (post-Minkowskian, or PM, approximation). As applications, we compute corrections to the scattering angle in a black hole collision due to dissipative effects to leading PM order, as well as the post-Newtonian (PN) corrections to the equations of motion of binary black holes in non-relativistic orbits, which represents the leading order finite size effect in the equations of motion. The methods developed here are also applicable to the case of more general compact objects, eg. neutron stars, where the magnitude of the dissipative effects depends on non-gravitational physics (e.g, the equation of state for nuclear matter).

scholarly journals Mathematical models of supersonic and intersonic crack propagation in linear elastodynamics

2021 ◽  
Author(s):  
Javier Bonet ◽  
Antonio J. Gil
Keyword(s):  
Kinetic Energy ◽  
Crack Propagation ◽  
Mathematical Models ◽  
Linear Elasticity ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Two Dimensions ◽  
Discontinuous Solutions ◽  
Linear Elasticity Theory ◽  
Intersonic Crack Propagation

AbstractThis paper presents mathematical models of supersonic and intersonic crack propagation exhibiting Mach type of shock wave patterns that closely resemble the growing body of experimental and computational evidence reported in recent years. The models are developed in the form of weak discontinuous solutions of the equations of motion for isotropic linear elasticity in two dimensions. Instead of the classical second order elastodynamics equations in terms of the displacement field, equivalent first order equations in terms of the evolution of velocity and displacement gradient fields are used together with their associated jump conditions across solution discontinuities. The paper postulates supersonic and intersonic steady-state crack propagation solutions consisting of regions of constant deformation and velocity separated by pressure and shear shock waves converging at the crack tip and obtains the necessary requirements for their existence. It shows that such mathematical solutions exist for significant ranges of material properties both in plane stress and plane strain. Both mode I and mode II fracture configurations are considered. In line with the linear elasticity theory used, the solutions obtained satisfy exact energy conservation, which implies that strain energy in the unfractured material is converted in its entirety into kinetic energy as the crack propagates. This neglects dissipation phenomena both in the material and in the creation of the new crack surface. This leads to the conclusion that fast crack propagation beyond the classical limit of the Rayleigh wave speed is a phenomenon dominated by the transfer of strain energy into kinetic energy rather than by the transfer into surface energy, which is the basis of Griffiths theory.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

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