Significance of Elastic Coupling for Stresses and Leakage in Frictional Contacts.

We study how the commonly neglected coupling of normal and in-plane elastic response affects tribological properties when Hertzian or randomly rough indenters slide past an elastic body. Compressibility-induced coupling is found to substantially increase maximum tensile stresses, which cause materials to fail, and to decrease friction such that Amontons' law is violated macroscopically even when it holds microscopically. Confinement-induced coupling increases friction and enlarges domains of high tension. Moreover, both types of coupling affect the gap topography and thereby leakage. Thus, coupling can be much more than a minor perturbation of a mechanical contact.

Structural lubricity of physisorbed gold clusters on graphite and its breakdown: Role of boundary conditions and contact lines.

The sliding motion of gold slabs adsorbed on a graphite substrate is simulated using molecular dynamics. The central quantity of interest is the mean lateral force, that is, the kinetic friction rather than the maximum lateral forces, which correlates with the static friction. For most setups, we find Stokesian damping to resist sliding. However, velocity-insensitive (Coulomb) friction is observed for finite-width slabs sliding parallel to the armchair direction if the bottom-most layer of the three graphite layers is kept at zero stress rather than at zero displacement. Although the resulting kinetic friction remains much below the noise produced by the erratic fluctuations of (conservative) forces typical for structurally lubric contacts, the nature of the instabilities leading to Coulomb friction could be characterized as quasi-discontinuous dynamics of the Moiré patterns formed by the normal displacements near a propagating contact line. It appears that the interaction of graphite with the second gold layer is responsible for the symmetry break occurring at the interface when a contact line moves parallel to the armchair rather than to the zigzag direction.

Modeling the surface topography dependence of friction, adhesion, and contact compliance.

The small-scale topography of surfaces critically affects the contact area of solids and thus the forces acting between them. Although this has long been known, only recent advances made it possible to reliably model interfacial forces and related quantities for surfaces with multiscale roughness. This article sketches both recent and traditional approaches to their mechanics, while addressing the relevance of nonlinearity and nonlocality arising in soft- and hard-matter contacts.

Scale-Dependent Friction-Coverage Relations and Nonlocal Dissipation in Surfactant Monolayers.

Surfactant molecules, known as organic friction modifiers (OFMs), are routinely added to lubricants to reduce friction and wear between sliding surfaces. In macroscale experiments, friction generally decreases as the coverage of OFM molecules on the sliding surfaces increases; however, recent nanoscale experiments with sharp atomic force microscopy (AFM) tips have shown increasing friction. To elucidate the origin of these opposite trends, we use nonequilibrium molecular dynamics (NEMD) simulations and study kinetic friction between OFM monolayers and an indenting nanoscale asperity. For this purpose, we investigate various coverages of stearamide OFMs on iron oxide surfaces and silica AFM tips with different radii of curvature. We show that the differences between the friction-coverage relations from macroscale and nanoscale experiments are due to molecular plowing in the latter. For our small tip radii, the friction coefficient and indentation depth both have a nonmonotonic dependence on OFM surface coverage, with maxima occurring at intermediate coverage. We rationalize the nonmonotonic relations through a competition of two effects (confinement and packing density) that varying the surface coverage has on the effective stiffness of the OFM monolayers. We also show that kinetic friction is not very sensitive to the sliding velocity in the range studied, indicating that it originates from instabilities. Indeed, we find that friction predominately originates from plowing of the monolayers by the leading edge of the tip, where gauche defects are created, while thermal dissipation is mostly localized in molecules toward the trailing edge of the tip, where the chains return to a more extended conformation.

Tactile perception of randomly rough surfaces.

Most everyday surfaces are randomly rough and self-similar on sufficiently small scales. We investigated the tactile perception of randomly rough surfaces using 3D-printed samples, where the topographic structure and the statistical properties of scale-dependent roughness were varied independently. We found that the tactile perception of similarity between surfaces was dominated by the statistical micro-scale roughness rather than by their topographic resemblance. Participants were able to notice differences in the Hurst roughness exponent of 0.2, or a difference in surface curvature of 0.8 [Formula: see text] for surfaces with curvatures between 1 and 3 [Formula: see text]. In contrast, visual perception of similarity between color-coded images of the surface height was dominated by their topographic resemblance. We conclude that vibration cues from roughness at the length scale of the finger ridge distance distract the participants from including the topography into the judgement of similarity. The interaction between surface asperities and fingertip skin led to higher friction for higher micro-scale roughness. Individual friction data allowed us to construct a psychometric curve which relates similarity decisions to differences in friction. Participants noticed differences in the friction coefficient as small as 0.035 for samples with friction coefficients between 0.34 and 0.45.

A mixed radial, angular, three-body distribution function as a tool for local structure characterization: Application to single-component structures.

A mixed radial, angular three-body distribution function g3(rBC, θABC) is introduced, which allows the local atomic order to be more easily characterized in a single graph than with conventional correlation functions. It can be defined to be proportional to the probability of finding an atom C at a distance rBC from atom B while making an angle θABC with atoms A and B, under the condition that atom A is the nearest neighbor of B. As such, our correlation function contains, for example, the likelihood of angles formed between the nearest and the next-nearest-neighbor bonds. To demonstrate its use and usefulness, a visual library for many one-component crystals is produced first and then employed to characterize the local order in a diverse body of elemental condensed-matter systems. Case studies include the analysis of a grain boundary, several liquids (argon, copper, and antimony), and polyamorphism in crystalline and amorphous silicon including that obtained in a tribological interface.

Why liquids can appear to solidify during squeeze-out - Even when they don't.

When liquids are squeezed out between two solid surfaces, they often exhibit layering, load-bearing ability, and a much increased viscosity. The combination of these phenomena is frequently interpreted as confinement-induced solidification. Here we propose that such behavior may often better be rationalized as the non-zero wavevector response of a pressurized liquid: bulk liquids contain structure even beyond the nanoscale as evidenced by their (damped) sinusoidal density correlations. Under confinement, this structure enables liquids to sustain non-isotropic stresses and thereby to carry load over a time span that is long enough for molecules to rearrange in the confined zone. In response to the load, viscosity can increase locally, in which case liquid flow is suppressed. This interpretation is supported by molecular-dynamics simulations of a key commercial base-oil component (1-decene trimer), which is squeezed out between a ridge and a substrate. The layering of the oil reflects the density correlations of the bulk liquid. At the same time, the confined liquid can sustain von Mises stresses exceeding locally 100 MPa over sufficiently long times for molecules to diffuse within the confined zone.

Entropy Can Bundle Nanowires in Good Solvents.

Surfaces with surface-bound ligand molecules generally attract each other when immersed in poor solvents but repel each other in good solvents. While this common wisdom holds, for example, for oleylamine-ligated ultrathin nanowires in the poor solvent ethanol, the same nanowires were recently observed experimentally to bundle even when immersed in the good solvent n-hexane. To elucidate the respective binding mechanisms, we simulate both systems using molecular dynamics. In the case of ethanol, the solvent is completely depleted at the interface between two ligand shells so that their binding occurs, as expected, via direct interactions between ligands. In the case of n-hexane, ligands attached to different nanowires do not touch. The binding occurs because solvent molecules penetrating the shells preferentially orient their backbone normal to the wire, whereby they lose entropy. This entropy does not have to be summoned a second time when the molecules penetrate another nanowire. For the mechanism to be effective, the ligand density appears to best be intermediate, that is, small enough to allow solvent molecules to penetrate, but not so small that ligands do not possess a clear preferred orientation at the interface to the solvent. At the same time, solvent molecules may be neither too large nor too small for similar reasons. Experiments complementing the simulations confirm the predicted trends.

Shear heating, flow, and friction of confined molecular fluids at high pressure.

Understanding the molecular-scale behavior of fluids confined and sheared between solid surfaces is important for many applications, particularly tribology where this often governs the macroscopic frictional response. In this study, nonequilibrium molecular dynamics simulations are performed to investigate the effects of fluid and surface properties on the spatially resolved temperature and flow profiles, as well as friction. The severe pressure and shear rate conditions studied are representative of the elastohydrodynamic lubrication regime. In agreement with tribology experiments, flexible lubricant molecules give low friction, which increases linearly with logarithmic shear rate, while bulky traction fluids show higher friction, but a weaker shear rate dependence. Compared to lubricants, traction fluids show more significant shear heating and stronger shear localization. Models developed for macroscopic systems can be used to describe both the spatially resolved temperature profile shape and the mean film temperature rise. The thermal conductivity of the fluids increases with pressure and is significantly higher for lubricants compared to traction fluids, in agreement with experimental results. In a subset of simulations, the efficiency of the thermostat in one of the surfaces is reduced to represent surfaces with lower thermal conductivity. For these unsymmetrical systems, the flow and the temperature profiles become strongly asymmetric and some thermal slip can occur at the solid-fluid interface, despite the absence of velocity slip. The larger temperature rises and steeper velocity gradients in these cases lead to large reductions in friction, particularly at high pressure and shear rate.

Determination of accurate, mean bond lengths from radial distribution functions.

The mean bond length d between a central atom and its nearest neighbors can be estimated from the position of the first peak in the radial distribution function g(r). However, as we demonstrate here, this estimate does not allow one to deduce temperature-induced changes in d. Instead, skewness has to be included into the analysis, which can be achieved, for example, via the skew normal distribution (SND). Fits to the first peak using the SND give bond length in good agreement with direct measurements of nearest-neighbor distribution functions in crystals as well as with a Voronoi-tessellation based detection of nearest-neighbors in liquids. While the location of the first peak in g(r) may shift to smaller values with increasing temperature for three studied liquids-argon, copper, and the bulk-metallic-glass (BMG) forming alloy Zr60Cu30Al10-we find our improved estimates of d to systematically increase with temperature in all cases. Recent conclusions on temperature-induced bond contractions in simple metallic or BMG-forming liquids may therefore have arisen from the neglect of skewness effects.

Constraints on phase stability, defect energies, and elastic constants of metals described by EAM-type potentials.

We demonstrate that the embedded-atom method and related potentials predict many dimensionless properties of simple metals to depend predominantly on a single coefficient µ, which typically lies between 0.3 and 0.45. Among other relations presented in this work, we find that [Formula: see text], [Formula: see text], and [Formula: see text] hold within 25% accuracy and also find a linear dependence of the melting temperature on µ. The used variables are cohesive energy E c, coordination number Z, vacancy energy E v, and bulk modulus B, while G is the average of ordinary and tetragonal shear modulus. We provide analytical arguments for these findings, which are obeyed reasonably well by several metals.

Dynamic shear force microscopy of viscosity in nanometer-confined hexadecane layers.

Hexadecane exhibits pronounced molecular layering upon confinement to gaps of a few nanometer width which is discussed for its role in boundary lubrication. We have probed the mechanical properties of the confined layers with the help of an atomic force microscope, by quasi-static normal force measurements and by analyzing the lateral tip motion of a magnetically actuated torsional cantilever oscillation. The molecular layering is modeled by a oscillatory force curve and the tip approach is simulated assuming thermal equilibrium correlations in the liquid. The shear response of the confined layers reveals gradually increasing stiffness and viscous dissipation for a decreasing number of confined layers.

Fluid leakage near the percolation threshold.

Percolation is a concept widely used in many fields of research and refers to the propagation of substances through porous media (e.g., coffee filtering), or the behaviour of complex networks (e.g., spreading of diseases). Percolation theory asserts that most percolative processes are universal, that is, the emergent powerlaws only depend on the general, statistical features of the macroscopic system, but not on specific details of the random realisation. In contrast, our computer simulations of the leakage through a seal--applying common assumptions of elasticity, contact mechanics, and fluid dynamics--show that the critical behaviour (how the flow ceases near the sealing point) solely depends on the microscopic details of the last constriction. It appears fundamentally impossible to accurately predict from statistical properties of the surfaces alone how strongly we have to tighten a water tap to make it stop dripping and also how it starts dripping once we loosen it again.

Charge-transfer potentials for ionic crystals: Cauchy violation, LO-TO splitting, and the necessity of an ionic reference state.

In this work, we study how including charge transfer into force fields affects the predicted elastic and vibrational Γ-point properties of ionic crystals, in particular those of rock salt. In both analytical and numerical calculations, we find that charge transfer generally leads to a negative contribution to the Cauchy pressure, P(C) ≡ C12 - C66, where C12 and C66 are elements of the elastic tensor. This contribution increases in magnitude with pressure for different charge-transfer approaches in agreement with results obtained with density functional theory (DFT). However, details of the charge-transfer models determine the pressure dependence of the longitudinal optical-transverse optical splitting and that for partial charges. These last two quantities increase with density as long as the chemical hardness depends at most weakly on the environment while experiments and DFT find a decrease. In order to reflect the correct trends, the charge-transfer expansion has to be made around ions and the chemical (bond) hardness has to increase roughly exponentially with inverse density or bond lengths. Finally, the adjustable force-field parameters only turn out meaningful, when the expansion is made around ions.

High-order sampling schemes for path integrals and Gaussian chain simulations of polymers.

In this work, we demonstrate that path-integral schemes, derived in the context of many-body quantum systems, benefit the simulation of Gaussian chains representing polymers. Specifically, we show how to decrease discretization corrections with little extra computation from the usual O(1/P(2)) to O(1/P(4)), where P is the number of beads representing the chains. As a consequence, high-order integrators necessitate much smaller P than those commonly used. Particular emphasis is placed on the questions of how to maintain this rate of convergence for open polymers and for polymers confined by a hard wall as well as how to ensure efficient sampling. The advantages of the high-order sampling schemes are illustrated by studying the surface tension of a polymer melt and the interface tension in a binary homopolymers blend.

Systematic analysis of Persson's contact mechanics theory of randomly rough elastic surfaces.

We systematically check explicit and implicit assumptions of Persson's contact mechanics theory. It casts the evolution of the pressure distribution Pr(p) with increasing resolution of surface roughness as a diffusive process, in which resolution plays the role of time. The tested key assumptions of the theory are: (a) the diffusion coefficient is independent of pressure p, (b) the diffusion process is drift-free at any value of p, (c) the point p = 0 acts as an absorbing barrier, i.e., once a point falls out of contact, it never re-enters again, (d) the Fourier component of the elastic energy is only populated if the appropriate wave vector is resolved, and (e) it no longer changes when even smaller wavelengths are resolved. Using high-resolution numerical simulations, we quantify deviations from these approximations and find quite significant discrepancies in some cases. For example, the drift becomes substantial for small values of p, which typically represent points in real space close to a contact line. On the other hand, there is a significant flux of points re-entering contact. These and other identified deviations cancel each other to a large degree, resulting in an overall excellent description for contact area, contact geometry, and gap distribution functions. Similar fortuitous error cancellations cannot be guaranteed under different circumstances, for instance when investigating rubber friction. The results of the simulations may provide guidelines for a systematic improvement of the theory.

Force microscopy of layering and friction in an ionic liquid.

The mechanical properties of the ionic liquid 1-butyl-1-methylpyrrolidinium tris(pentafluoroethyl) trifluorophosphate ([Py1,4][FAP]) in confinement between a SiOx and a Au(1 1 1) surface are investigated by means of atomic force microscopy (AFM) under electrochemical control. Up to 12 layers of ion pairs can be detected through force measurements while approaching the tip of the AFM to the surface. The particular shape of the force versus distance curve is explained by a model for the interaction between tip, gold surface and ionic liquid, which assumes an exponentially decaying oscillatory force originating from bulk liquid density correlations. Jumps in the tip-sample distance upon approach correspond to jumps of the compliant force sensor between branches of the oscillatory force curve. Frictional force between the laterally moving tip and the surface is detected only after partial penetration of the last double layer between tip and surface.

Solvent-induced immiscibility of polymer brushes eliminates dissipation channels.

Polymer brushes lead to small friction and wear and thus hold great potential for industrial applications. However, interdigitation of opposing brushes makes them prone to damage. Here we report molecular dynamics simulations revealing that immiscible brush systems can form slick interfaces, in which interdigitation is eliminated and dissipation strongly reduced. We test our findings with friction force microscopy experiments on hydrophilic and hydrophobic brush systems in both symmetric and asymmetric setups. In the symmetric setup both brushes are chemically alike, while the asymmetric system consists of two different brushes that each prefer their own solvent. The trends observed in the experimentally measured force traces and the friction reduction are similar to the simulations and extend to fully immersed contacts. These results reveal that two immiscible brush systems in mechanical contact slide at a fluid-fluid interface while having load-bearing ability. This makes them ideal candidates for tribological applications.

Single-asperity contact mechanics with positive and negative work of adhesion: Influence of finite-range interactions and a continuum description for the squeeze-out of wetting fluids.

In this work, single-asperity contact mechanics is investigated for positive and negative work of adhesion Δγ. In the latter case, finite-range repulsion acts in addition to hard-wall constraints. This constitutes a continuum model for a contact immersed in a strongly wetting fluid, which can only be squeezed out in the center of the contact through a sufficiently large normal load F N. As for positive work of adhesion, two stable solutions can coexist in a finite range of normal loads. The competing solutions can be readily interpreted as contacts with either a load-bearing or a squeezed-out fluid. The possibility for coexistence and the subsequent discontinuous wetting and squeeze-out instabilities depend not only on the Tabor coefficient µT but also on the functional form of the finite-range repulsion. For example, coexistence and discontinuous wetting or squeeze-out do not occur when the repulsion decreases exponentially with distance. For positive work of adhesion, the normal displacement mainly depends on F N, Δγ, and µT but - unlike the contact area - barely on the functional form of the finite-range attraction. The results can benefit the interpretation of atomic force microscopy in liquid environments and the modeling of multi-asperity contacts.