Separating anisotropic and isotropic friction between atomic force microscope tips and atomically flat surfaces

Anisotropic vs. isotropic friction: New theoretical results verified experimentally exhibited by a horizontal pendulum on the rotating disk

Friction plays a crucial role in both natural phenomena, from the flow of blood cells to earthquakes, and technological applications, from car engines to wind turbines. One of the most fundamental aspects of tribology is friction anisotropy, that is, the dependence of the friction force vector on the direction of sliding. Even when two identical surfaces slide against each other, differences in sliding direction can lead to significantly different friction forces. While atomistic and semi-empirical models provide a good understanding of friction and friction anisotropy at the molecular and macroscale levels, a comprehensive understanding at the nano- and microscale remains elusive. Unravelling the mechanisms of friction anisotropy at these intermediate length scales is crucial for bridging the gap between the current atomistic and macroscale models, as well as for advancing technological applications, such as nano-/micro-electromechanical systems (NEMS/MEMS). One experimental technique which has significantly contributed to the study of nano- and micro-scale friction anisotropy is scanning probe microscopy, particularly the form of atomic force microscopy (AFM). AFM enables investigations at the nanometre-scale resolution, providing at equilibrium topographical, physical, and chemical information of interfaces with atomic precision. AFM can also measure friction forces with pN-level sensitivity while operating in vacuum, air or fluid environments. The versatility of AFM and its applicability to both soft and hard materials have made it an indispensable tool for understanding the nano- and microscale mechanisms of friction. In this review, we examine the contributions of AFM-based techniques to the study of friction anisotropy. First, we summarise key AFM findings on friction anisotropy arising from the periodic corrugation of atomically flat crystals, quasicrystals, 2D materials and organic materials. In the second part, we explore friction anisotropy mechanisms influenced by the presence of solid or fluid adsorbates, such as polymers or liquid lubricants. By synthesising insights from the last 30 years of research, our review contributes to a deeper understanding of friction anisotropy, identifying common mechanisms across the diverse systems. This knowledge will not only refine theoretical models but also drive technological advancements, in a wide range of applications from biomedical devices and 3D printing to engines and advanced lubricant formulations.

The paper aims the determination of the friction force by means of external friction stress, at the severe plastic deformation processing using cyclic closed-die forging method. It is known that the total force used at the severe plastic deformation by the method of multiaxial forging is being composed by the deformation force itself and the friction force between the semi-product and the deformation tools. Once the friction stresses known, for a certain material, one can determine the friction force corresponding for a given deformation of a semi-product of a particular shape and sizes. By means of the flowing curve of the semi-product material one can determine the deformation force, which together with the friction force give the total necessary force for a deformation and so one can choose the necessary equipment for the processing of the material by severe plastic deformation. For this purpose it has been severely plastic deformed by the method of multiaxial forging, a semi-product having the sizes 10x10x20 mm, the finished part having the same sizes and shape. It has been measured the deformation force and the extraction force of the finished part from the cavity of the active plate, the late being used for the determination of the friction stress between the semi-product and the active plate.

We briefly review the nanomechanical studies of ultralow friction in the following carbon hybrid systems: atomic force microscopy (AFM) tip on graphite surface, AFM tip on C60/graphite, graphite on graphite surface, graphite/C60/graphite, and C60 intercalated graphite. For the atomic and flake frictions, frictional force maps are compared between simulations and experiments, which can be explained by stick-slip motion of the tip apex atom and flake. For the graphite/C60/graphite system, superlubricity appears, where the maximum static frictional forces have finite values but denote that dynamical frictional forces are zero within the resolution of the experiment. Furthermore, for the C60 intercalated graphite system, greater superlubricity appears. It is clarified that fullerene intercalated graphite films exhibit ultralow average friction force, and excellent friction coefficients μ < 0.001. Our results propose one of the simple guidelines of designing a practical superlubric system - reduction of the contact area between intercalated C60 and graphite sheet to the point contact. Clearly, the C60 intercalated graphite system will contribute to solving energy and environmental problems in the future.

Generation mechanism of friction anisotropy by surface texturing under boundary lubrication

Frictional asymmetry due to the tilt of carbonate ions at (104) surface of calcite (CaCO3) was detected with frictional force microscopy. The asymmetry signal was recorded by scanning the probe across the boundary between two surfaces of oppositely placed crystals in [42] direction. Observed asymmetry was in striking contrast with previous results for tilted SO bonds of CaSO4(100), lower friction being observed when the probe was scanned against the tilt. The difference was explained by the tilt angles of CO and SO bonds, which are described as mass-spring systems, from surface normal. More tilted CO bonds of calcite support the normal load mainly by the reaction against bending of the springs, while less tilted SO bonds support the load by the reaction against compression of the springs. As was expected, the asymmetry signal was strongest along the [42] direction, while no asymmetry was observed along the [010] direction. Compared to the case of CaSO4, the asymmetry signal at the calcite surface took a large proportion of the total friction. The anisotropy in the total friction was also studied at the same surface, weakest total friction being observed along the [010] direction. Travelling straight in that direction, the tip atom at the probe surface frequently meets bridge sites where they can interact with two oxygen atoms of the carbonate ions. The result was in accordance with a similar experiment with a corrugated CaSO4(001) surface.

Using friction force microscopy (FFM) under controlled environments, we have systematically investigated the humidity effect on the frictional properties of two important classes of self-assembled monolayers (SAMs), i.e., N-octadecyltrimethoxysilane (OTE, CH3(CH2)17Si(OCH3)3) on SiO2(OTE/SiO2), and N-alkanethiols on Au(111), together with their respective substrates. Experimental results show that both OTE and alkylthiol SAMs can decrease the friction force between a Si3N4 atomic force microscope (AFM) tip and substrates. The nearly humidity-independent friction of the two kinds of SAMs indicates that these SAMs are ideal lubricants in applications of micro-electro-mechanical systems (MEMS) under different environments. The humidity dependence—as the humidity increases, the friction first increases and then decreases—of the two substrates, SiO2 and Au(111), can be explained by the adsorption of water. The decrease in the friction at high humidity is attributed to the low viscosity in the multilayers of water, while the increase in the friction at low humidity can be explained by the high viscosity between the water monolayer and the surfaces (AFM tip and sample), possibly due to the confinement effects. The effect of modification of the AFM tip with alkanethiol molecules on the humidity dependence of Au(111) friction has also been investigated.

The load effect on the anisotropic friction property of gecko seta arrays have been experimentally investigated on a homemade micro adhesive and friction force detect device with isolated seta arrays. The result shows that when sliding against the direction of the seta curvature to grip out, the friction force is proportional to the normal load with a friction coefficient of about 0.6. When sliding along the direction of the seta curvature to grip in, the normal preload force could be fully or partly transformed into adhesion force and repulsive force while friction force rapidly rose with the increment of the applied preload. Under the same normal preload, the lateral friction force in grip in is more than twice of that in grip out. These properties of anisotropy in friction and adhesion are determined by the micro and nano-structures of setae.

This research regards to a two-dimensional lateral pushing nanomanipulation using Atomic Force Microscope (AFM). Yet a reliable control of the AFM tip position during the AFM-based manipulation process is a chief issue since the tip can jump over the target nanoparticle and then the process can fail. However, a detailed Modeling and understanding of the interaction forces on the AFM tip is important for prosperous manipulation control and a nanometer resolution tip positioning. In the proposed model, Lund-Grenoble (LuGre) dynamic friction model is used as friction force on the contact surface between the nanoparticle and the substrate. This model leads to a stick-slip behavior of the nanoparticle that is so similar to the experimental behavior in nanoscale. Derjaguin interaction force is applied between the AFM tip and the nanoparticle which considers both attractive and repulsive interactions. The AFM is modeled by lumped-parameters model. A controller is designed based on the proposed dynamic model in order for positioning the AFM tip during a desired nanomanipulation task. Optimal sliding mode approach is used to design the controller. In this approach sliding surface which is used in the sliding mode approach is selected optimally based on the linear quadratic (LQ) method.

Perturbation theory for the angular pair correlation function g(r12 ω 1 ω 2), using a fluid with isotropic intermolecular forces as the reference system, is applied to the calculation of a variety of macroscopic properties. Comparisons with experiment are made for methane, oxygen and nitrogen (and carbon monoxide for infra-red and Raman band moments) in the dense fluid and liquid states. Theoretical expressions are given and calculations made for thermodynamic properties (isothermal compressibility, pressure, configurational energy, entropy and specific heat) both along and away from the vapour-liquid co-existence curve, for infra-red and Raman band moments, and for neutron scattering cross sections. Excellent agreement with experiment is obtained for all properties, except for the infra-red and Raman band moments; this latter comparison is inconclusive because of large experimental uncertainties. The anisotropic intermolecular forces are found to have very little effect on the liquid isothermal compressibility, in agreement with the first-order theory. Molecular anisotropy has a relatively small effect on the configurational energy and on the Helmholtz free energy, but the effect is large for pressure and specific heat. The pressure is more sensitive to short-range anisotropic forces than the other properties, whereas the specific heat is particularly sensitive to the long-range anisotropic forces. Mean squared torques (derived from infra-red and Raman band moments) are very sensitive to the strengths of the anisotropic forces, and are more sensitive to higher terms in the multipole series than are the other properties. The structure factors for oxygen and nitrogen are found to be little affected by the anisotropic forces.

Determination of the belt force before the gross slip

Friction anisotropy in confined alkanes: Linear and branched molecules

Using liquid-cell atomic force microscopy, we investigate aqueous solutions of alkyltrimethylammonium halide surfactants at the Au111 surface. The long, micellar surfactant surface aggregates cover the gold surface completely and exhibit two types of orientational order for chloride and bromide counterions, respectively. We observe lateral forces perpendicular to the scanning direction, which we explain by anisotropic friction between the probe and the oriented micelles. Conversely, we show that these friction forces can be employed to modify the spatial conformation of the micellar adlayer. Where previous methods have failed to provide control over the orientation down to the level of individual micelles, we use this technique to achieve a very high degree of order over more than 100 micelle diameters.

We used an ultrahigh-vacuum atomic force microscope (AFM) to measure lateral forces and conductivity simultaneously as a function of the applied normal force for nanometer-sized elastic contacts. Metal-coated or bare Si AFM tips are used on cleaved ${\mathrm{NbSe}}_{2}$ or graphite surfaces. Results are used to compare various means of obtaining the tip-sample contact area ${(A}_{0}).$ We find that simple continuum models can give a reasonable description of the mechanical behavior of the contact. Specifically, the Maugis-Dugdale model [D. Maugis, J. Colloid Interface Sci. 150, 243 (1992)] provides a good basis for describing the elastic contact between an AFM tip and a smooth sample. The theoretical variation in contact radius with load is in good agreement with the experimental variation in friction force, conductivity, and lateral tip-sample contact stiffness. To find the contact area ${A}_{0},$ the best approaches appear to be either to fit the applied force data to an appropriate continuum model (provided the contact is elastic) or to measure the lateral tip-sample contact stiffness. In principle we show that conduction AFM methods can be used to find ${A}_{0}$ for Ohmic contacts. However, the uncertainty in the conduction properties of available AFM tips means that at present the absolute value of ${A}_{0}$ cannot be found with confidence. In this regard the use of metal-coated tips can often be misleading for conduction and mechanical measurements because metal wears rapidly off all or some of the tip apex.

In this paper, the performance of a multi-unit friction damper with high-tension bolts tightened via coned disc springs was experimentally investigated, and the response control effects achieved by the friction damper were numerically assessed. Elemental tests were performed to obtain the basic characteristics of dampers composed of two friction units. The dampers exhibited a stable rigid-plastic restoring force characteristic without significant degradation of the frictional force even under repetitive loading operations. In full-scale tests, the performance of a brace-type damper composed of eight or 10 friction units and incorporated into a steel frame was investigated. The brace-type damper demonstrated stable performance and showed no remarkable decrease in the sliding force, even under repeated loading. The damper was shown to produce a total frictional force approximately proportional to the number of the friction units. Thus, the total frictional force of the damper can be estimated as the sum of the contributions of the friction units. Moreover, adopting multiple friction units and assembling them permit the damper to achieve a high total frictional force capacity. Earthquake response analysis was conducted using a 30-story high-rise building model incorporating the brace-type dampers to assess their performance against various earthquake motions, including long-period, long-duration motions and pulse-like motions. By installing the high-capacity brace-type dampers into the two spans out of 12 spans for each floor of the main frame, a response reduction effect was obtained in most analytical cases compared to the model without dampers.