Simulations of the kinetic friction due to adsorbed surface layers

Simulations of the kinetic friction due to a layer of adsorbed molecules between two crystalline surfaces are presented. The adsorbed layer naturally produces friction that is consistent with Amontons' laws and insensitive to parameters that are not controlled in experiments. The kinetic friction rises logarithmically with velocity as in many experimental systems. Variations with potential parameters and temperature follow variations in the static friction. This correlation is understood through analogy with the Tomlinson model and the trends are explained with a hard-sphere picture.Comment: 8 pages, 6 figures, submitted to Tribology Letter

Capillary Adhesion at the Nanometer Scale

Molecular dynamics simulations are used to study the capillary adhesion from a nonvolatile liquid meniscus between a spherical tip and a flat substrate. The atomic structure of the tip, the tip radius, the contact angles of the liquid on the two surfaces, and the volume of the liquid bridge are varied. The capillary force between the tip and substrate is calculated as a function of their separation h. The force agrees with continuum predictions for h down to ~ 5 to 10nm. At smaller h, the force tends to be less attractive than predicted and has strong oscillations. This oscillatory component of the capillary force is completely missed in the continuum theory, which only includes contributions from the surface tension around the circumference of the meniscus and the pressure difference over the cross section of the meniscus. The oscillation is found to be due to molecular layering of the liquid confined in the narrow gap between the tip and substrate. This effect is most pronounced for large tip radii and/or smooth surfaces. The other two components considered by the continuum theory are also identified. The surface tension term, as well as the meniscus shape, is accurately described by the continuum prediction for h down to ~ 1nm, but the capillary pressure term is always more positive than the corresponding continuum result. This shift in the capillary pressure reduces the average adhesion by a factor as large as 2 from its continuum value and is found to be due to an anisotropy in the pressure tensor. The cross-sectional component is consistent with the capillary pressure predicted by the continuum theory (i.e., the Young-Laplace equation), but the normal pressure that determines the capillary force is always more positive than the continuum counterpart.Comment: 16 pages, 14 figure

Defining Contact at the Atomic Scale

Molecular dynamics simulations are used to study different definitions of contact at the atomic scale. The roles of temperature, adhesive interactions and atomic structure are studied for simple geometries. An elastic, crystalline substrate contacts a rigid, atomically flat surface or a spherical tip. The rigid surface is formed from a commensurate or incommensurate crystal or an amorphous solid. Spherical tips are made by bending crystalline planes or removing material outside a sphere. In continuum theory the fraction of atomically flat surfaces that is in contact rises sharply from zero to unity when a load is applied. This simple behavior is surprisingly difficult to reproduce with atomic scale definitions of contact. Due to thermal fluctuations, the number of atoms making contact at any instant rises linearly with load over a wide range of loads. Pressures comparable to the ideal hardness are needed to achieve full contact at typical temperatures. A simple harmonic mean-field theory provides a quantitative description of this behavior and explains why the instantaneous forces on atoms have a universal exponential form. Contact areas are also obtained by counting the number of atoms with a time-averaged repulsive force. For adhesive interactions, the resulting area is nearly independent of temperature and averaging interval, but usually rises from zero to unity over a range of pressures that is comparable to the ideal hardness. The only exception is the case of two identical commensurate surfaces. For nonadhesive surfaces, the mean pressure is repulsive if there is any contact during the averaging interval $\Delta t$. The associated area is very sensitive to $\Delta t$ and grows monotonically. Similar complications are encountered in defining contact areas for spherical tips.Comment: 18 pages, 11 figure

Mapping molecular models to continuum theories for partially miscible fluids

We map molecular dynamics simulations of fluid-fluid interfaces onto mesoscale continuum theories for partially miscible fluids. Unlike most previous work, we examine not only the interface order parameter and density profiles, but also the stress. This allows a complete mapping from the length scales of molecular dynamics simulations onto a mesoscale model suitable for a lattice Boltzmann or other mesoscale simulation method. Typical assumptions of mesoscale models, such as incompressibility, are found to fail at the interface, and this has a significant impact on the surface tension. Spurious velocities, found in a number of discrete models of curved interfaces, are found to be minimized when the parameters of the mesoscopic model are made consistent with molecular dynamics results. An improved mesoscale model is given and demonstrated to produce results consistent with molecular dynamics simulations for interfaces with widths down to near molecular size.Comment: 43 pages, 17 figures, RevTex

Computer Simulations of Friction, Lubrication and Wear

An overview of computer simulations of tribology is presented. The chapter begins with a brief overview of simulation techniques and the special requirements for simulations of tribological processes. Then simple one-dimensional models of friction between crystalline surfaces are introduced to illustrate general features of friction, such as the importance of metastability and the effect of commensurability. Next two- and three-dimensional studies of dry sliding between crystalline surfaces are described, and compared to scanning probe experiments and measurements of the friction on adsorbed monolayers. Lubrication is then discussed, starting from thick films and describing the breakdown in bulk hydrodynamics as the thickness of the lubricant decreases to molecular scales. Deviations from the usual no-slip boundary condition are quantified and the onset of solid behavior in molecularly thick films is described. The possibility that solidification of thin layers of adventitious carbon is responsible for the prevalence of static friction is explored. The final sections describe stick-slip motion, tribochemical reactions, machining, and the evolution of microstructure in sliding contacts.Comment: Review chapter for the Handbook of Modern Tribology edited by Bharat Bhushan (CRC Press), 42 pages, 16 figure

Chain Ends and the Ultimate Strength of Polyethylene Fibers

We use large scale molecular dynamics (MD) simulations to determine the tensile yield mechanism of orthorhombic polyethylene (PE) crystals with finite chains spanning $10^2-10^4$ carbons in length. We find the yield stress $\sigma_y$ saturates for long chains at 6.3 GPa, agreeing well with experiments. We show chains do not break but always yield by slip, after nucleation of 1D dislocations at chain ends. Dislocations are accurately described by a Frenkel-Kontorova model parametrized by the mechanical properties of an ideal crystal. We compute a dislocation core size $\xi\approx25$\AA\ and determine the high and low strain rate limits of $\sigma_y$. Our results suggest characterizing the 1D dislocations of polymer crystals as an efficient method for numerically predicting the ultimate tensile strength of aligned fibers

The effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions

Molecular dynamics simulations with varying damping are used to examine the effects of inertia and spatial dimension on sheared disordered solids in the athermal, quasistatic limit. In all cases the distribution of avalanche sizes follows a power law over at least three orders of magnitude in dissipated energy or stress drop. Scaling exponents are determined using finite-size scaling for systems with thousands to millions of particles. Three distinct universality classes are identified corresponding to overdamped and underdamped limits, as well as a crossover damping that separates the two regimes. For each universality class, the exponent describing the avalanche distributions is the same in two and three dimensions. The spatial extent of plastic damage is proportional to the energy dissipated in an avalanche. Both rise much more rapidly with system size in the underdamped limit where inertia is important. Inertia also lowers the mean energy of configurations sampled by the system and leads to an excess of large events like that seen in earthquake distributions for individual faults. The distribution of stress values during shear narrows to zero with increasing system size and may provide useful information about the size of elemental events in experimental systems. For overdamped and crossover systems the stress variation scales inversely with the square root of the system size. For underdamped systems the variation is determined by the size of the largest events.Comment: 17 pages, 13 figure

Stretching of Proteins in the Entropic Limit

Mechanical stretching of six proteins is studied through molecular dynamics simulations. The model is Go-like, with Lennard-Jones interactions at native contacts. Low temperature unfolding scenarios are remarkably complex and sensitive to small structural changes. Thermal fluctuations reduce the peak forces and the number of metastable states during unfolding. The unfolding pathways also simplify as temperature rises. In the entropic limit, all proteins show a monotonic decrease of the extension where bonds rupture with their separation along the backbone (contact order).Comment: RevTex, 5 pages, 5 figures, to appear in Phys. Rev.

Thermal Folding and Mechanical Unfolding Pathways of Protein Secondary Structures

Mechanical stretching of secondary structures is studied through molecular dynamics simulations of a Go-like model. Force vs. displacement curves are studied as a function of the stiffness and velocity of the pulling device. The succession of stretching events, as measured by the order in which contacts are ruptured, is compared to the sequencing of events during thermal folding and unfolding. Opposite cross-correlations are found for an $\alpha$-helix and a $\beta$-hairpin structure. In a tandem of two $\alpha$-helices, the two constituent helices unravel nearly simultaneously. A simple condition for simultaneous vs. sequential unraveling of repeat units is presented.Comment: 12 pages, 17 figure

Thermal effects in stretching of Go-like models of titin and secondary structures

The effect of temperature on mechanical unfolding of proteins is studied using a Go-like model with a realistic contact map and Lennard-Jones contact interactions. The behavior of the I27 domain of titin and its serial repeats is contrasted to that of simple secondary structures. In all cases thermal fluctuations accelerate the unraveling process, decreasing the unfolding force nearly linearly at low temperatures. However differences in bonding geometry lead to different sensitivity to temperature and different changes in the unfolding pattern. Due to its special native state geometry titin is much more thermally and elastically stable than the secondary structures. At low temperatures serial repeats of titin show a parallel unfolding of all domains to an intermediate state, followed by serial unfolding of the domains. At high temperatures all domains unfold simultaneously and the unfolding distance decreases monotonically with the contact order, that is the sequence distance between the amino acids that form the native contact.Comment: 38 pages, 17 figures, to appear in Protein