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.

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.

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.

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.

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.

Redox reactions with empirical potentials: atomistic battery discharge simulations.

Batteries are pivotal components in overcoming some of today's greatest technological challenges. Yet to date there is no self-consistent atomistic description of a complete battery. We take first steps toward modeling of a battery as a whole microscopically. Our focus lies on phenomena occurring at the electrode-electrolyte interface which are not easily studied with other methods. We use the redox split-charge equilibration (redoxSQE) method that assigns a discrete ionization state to each atom. Along with exchanging partial charges across bonds, atoms can swap integer charges. With redoxSQE we study the discharge behavior of a nano-battery, and demonstrate that this reproduces the generic properties of a macroscopic battery qualitatively. Examples are the dependence of the battery's capacity on temperature and discharge rate, as well as performance degradation upon recharge.

Self-affine elastic contacts: percolation and leakage.

We study fluid flow at the interfaces between elastic solids with randomly rough, self-affine surfaces. We show by numerical simulation that elastic deformation lowers the relative contact area at which contact patches percolate in comparison to traditional approaches to seals. Elastic deformation also suppresses leakage through contacts even far away from the percolation threshold. Reliable estimates for leakage can be obtained by combining Persson's contact mechanics theory with a slightly modified version of Bruggeman's effective-medium solution of the Reynolds equation.

Evidence for electronic gap-driven metal-semiconductor transition in phase-change materials.

Phase-change materials are functionally important materials that can be thermally interconverted between metallic (crystalline) and semiconducting (amorphous) phases on a very short time scale. Although the interconversion appears to involve a change in local atomic coordination numbers, the electronic basis for this process is still unclear. Here, we demonstrate that in a nearly vacancy-free binary GeSb system where we can drive the phase change both thermally and, as we discover, by pressure, the transformation into the amorphous phase is electronic in origin. Correlations between conductivity, total system energy, and local atomic coordination revealed by experiments and long time ab initio simulations show that the structural reorganization into the amorphous state is driven by opening of an energy gap in the electronic density of states. The electronic driving force behind the phase change has the potential to change the interconversion paradigm in this material class.

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.

Friction of wrinkles.

Sufficiently thin elastic sheets wrinkle when they are in contact with a small adhesive counterbody. Despite significant progress on the dynamics of wrinkle formation and morphology, little is known about how wrinkles impede the relative sliding motion of the counterbody. Using molecular dynamics we demonstrate that instabilities are likely to occur during sliding when the wrinkle pattern has asymmetries not present in the counterbody. The instabilities then cause Coulomb's friction law. The behavior can be rationalized in terms of simple models for multistable elastic manifolds.

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.

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.

Non-bonded force field for the interaction between metals and organic molecules: a case study of olefins on aluminum.

In this work, we parameterize an empirical potential for the interaction between organic molecules and metal surfaces via force matching. This is done by pursuing a self-consistent approach similar to the ones used for equilibrium simulations; however, special attention is paid to the suitability of the resulting potential for tribological (non-equilibrium) situations. Specifically, we study olefin molecules confined between two aluminum surfaces under realistic pressures and shear rates. We find that the Buckingham potential produces better agreement with the first principle data than other force fields. While our training set only contains hexene molecules, we find that the standard error in the fitted olefin-aluminum interaction increases only by a factor of 1.15 when the force field is applied to butene, octene, and decene. Including mirror charges into the treatment only marginally improves fits. While olefins on aluminum is merely a special case, the proposed methodology can be used to parameterize any other interaction between polymers and metal surfaces for use in tribological simulations.

Smart materials behavior in phosphates: role of hydroxyl groups and relevance to antiwear films.

The elastic properties of materials under high pressure are relevant to the understanding and performance of many systems of current interest, for example, in geology and tribology. Of particular interest is the origin of the dramatic increase in modulus with increasing pressure, a response which is also called "smart materials behavior." In this context, simple phosphate-containing materials have been studied experimentally and theoretically, and the origins of this behavior have been associated with factors such as coordination of the cations and changes in the degree of polymerization and hydrogenation of the phosphate units. In the present paper we extend the former analysis on simple metal phosphate model compounds to so-called thermal films, an intermediate stage in the formation of effective antiwear films. The material was produced by heating a commercial zinc dialkyldithiophosphate (ZDDP), a common antiwear additive in lubricating oils, in poly-alpha-olefin base oil solutions to 150 degrees C, a process known to produce the thermal films. Its structure and equation of state were studied by means of x-ray diffraction and IR synchrotron radiation techniques during compression up to 25 GPa in a diamond anvil cell as well as during the subsequent decompression. As is the case for the simple metal phosphates, we find that the thermal films are relatively soft at low pressures but stiffen rapidly and ultimately amorphize irreversibly at high pressure. However, in addition to phase transformations involving cation sites occurring in the metal phosphates studied previously, thermal films undergo displacive transitions associated with instabilities of the hydroxyl groups. These results may imply that ZDDP ligands and those of the transformed materials not only affect ZDDP decomposition rate in engines but also the mechanical properties of the resulting antiwear films.

A comparative study of the centroid and ring-polymer molecular dynamics methods for approximating quantum time correlation functions from path integrals.

The problems of ergodicity and internal consistency in the centroid and ring-polymer molecular dynamics methods are addressed in the context of a comparative study of the two methods. Enhanced sampling in ring-polymer molecular dynamics (RPMD) is achieved by first performing an equilibrium path integral calculation and then launching RPMD trajectories from selected, stochastically independent equilibrium configurations. It is shown that this approach converges more rapidly than periodic resampling of velocities from a single long RPMD run. Dynamical quantities obtained from RPMD and centroid molecular dynamics (CMD) are compared to exact results for a variety of model systems. Fully converged results for correlations functions are presented for several one dimensional systems and para-hydrogen near its triple point using an improved sampling technique. Our results indicate that CMD shows very similar performance to RPMD. The quality of each method is further assessed via a new chi(2) descriptor constructed by transforming approximate real-time correlation functions from CMD and RPMD trajectories to imaginary time and comparing these to numerically exact imaginary time correlation functions. For para-hydrogen near its triple point, it is found that adiabatic CMD and RPMD both have similar chi(2) error.