Towards an atomistic understanding of solid friction by computer simulations
Friction between two solid bodies in sliding motion takes place on a large spectrum of length and time scales: From the nanometer/second scale in an atomic force microscope up to the extremely macroscopic scales of tectonic motion. Despite our familiarity with friction, fundamental questions about its atomistic origins remain unanswered. Phenomenological laws that describe the friction in many systems were published more than 300 years ago by Amontons: The frictional force is proportional to the applied load and independent of the apparent area of contact. The atomistic origins of this simple law is still controversial. Many explanations, which seemed to be well-established until recently, …
On quantum effects near the liquid-vapor transition in helium
The liquid-vapor transition in He-3 and He-4 is investigated by means of path-integral molecular dynamics and the quantum virial expansion. Both methods are applied to the critical isobar and the critical isochore. While previous path-integral simulations have mainly considered the lambda transition and superfluid regime in He-4, we focus on the vicinity of the critical point and obtain good agreement with experimental results for the molar volume and the internal energy down to subcritical temperatures. We find that an effective classical potential that properly describes the two-particle radial distribution function exhibits a strong temperature dependence near the critical temperature. T…
Path-integral Monte Carlo study of crystalline Lennard-Jones systems.
The capability of the path-integral Monte Carlo (PIMC) method to describe thermodynamic and structural properties of solids at low temperatures is studied in detail, considering the noble-gas crystals as examples. In order to reduce the systematic limitations due to finite Trotter number and finite particle number we propose a combined Trotter and finite-size scaling. As a special application of the PIMC method we investigate $^{40}\mathrm{Ar}$ at constant volume and in the harmonic approximation. Furthermore, isotope effects in the lattice constant of $^{20}\mathrm{Ne}$ and $^{22}\mathrm{Ne}$ are computed at zero pressure. The obtained results are compared with classical Monte Carlo result…
Theory and Simulations of Friction between Flat Surfaces Lubricated by Submonolayers
Recent simulations suggest that wearless friction between two solid surfaces can only be obtained if the two surfaces are commensurate or if they are lubricated by a film. Some simple theoretical arguments are given why the presence of a submonolayer film between two solids leads to friction. Possible implications of the symmetry of the confining walls on the tribological properties of the system are then investigated in the presence of a thin film by means of molecular dynamics simulation. Erratic stick-slip motion of the incommensurate system and oscillating friction forces for the commensurate system in the sliding regime are observed.
Gradual freezing of orientational degrees of freedom in cubicAr1−x(N2)xmixtures
The mixed crystal ${\mathrm{Ar}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$(${\mathrm{N}}_{2}$${)}_{\mathit{x}}$ is studied by Monte Carlo (MC) methods for x=0.33, 0.67, and 1.0 over a wide range of temperatures. For x=1 we find first-order transition from ordered cubic to disordered cubic, while for x=0.33 and x=0.67 we find broad nonuniform distribution functions of the local quadrupole Edwards-Anderson order parameter at low temperature. The short-range order of the quadrupolar mass distribution of the ${\mathrm{N}}_{2}$ molecules in the mixed systems is different from that observed in the pure ${\mathrm{N}}_{2}$ crystal, although the fcc symmetry has been chosen for the translational degrees…
On the tribology and rheology of polymer brushes in good solvent conditions: a molecular dynamics study
Tribological and rheological properties of two polymer brushes in relative sliding motion and good solvent conditions are investigated by means of molecular dynamics (MD) simulations. The lateral forces between the brushes are found to decrease logarithmically with increasing relative sliding velocity v0 over a range of more than one decade in v0. We also observe an almost logarithmic relaxation of the end-to-end distance vector that occurs after sliding is stopped. The coincidence of these logarithmic dependencies support the picture that friction between polymer brushes is small due to the retraction of the polymers from the interpenetration zone. The shear stress relaxes almost instantly…
On new efficient algorithms for PIMC and PIMD
Abstract The properties of various algorithms, estimators, and high-temperature density matrix (HTDM) decompositions relevant for path integral simulations are discussed. It is shown that Fourier accelerated path integral molecular dynamics (PIMD) completely eliminates slowing down with increasing Trotter number P . A new primitive estimator of the kinetic energy for use in PIMD simulations is found to behave less pathologically than the original virial estimator. In particular, its variance does not increase significantly with P . Two non-primitive HTDM decompositions are compared as well: one decomposition used in the Takahashi Imada algorithm and another one based on an effective propaga…
Low-temperature anharmonic lattice deformations near rotator impurities: A quantum Monte Carlo approach.
At zero temperature the equilibrium structures of a system consisting of a quantum rotator (${\mathrm{N}}_{2}$) embedded in a relaxing lattice (Ar) surrounding are studied with a variational approach. With symmetric wave functions (para-${\mathrm{N}}_{2}$), we obtain a cubic lattice deformation near the rotator, while with antisymmetric wave functions (ortho-${\mathrm{N}}_{2}$), we obtain a tetragonal lattice deformation forming a stable oriented ground state. At low temperatures, we investigate the properties of this system with a quantum Monte Carlo simulation. On top of the tetragonal deformation the width of the nearest-neighbor oscillations follows classical ``scaling'' laws according …
Irreversibility of the pressure-induced phase transition of quartz and the relation between three hypothetical post-quartz phases
Our atomistic computer simulations mainly based on classical force fields suggest that the pressure-induced transition from $\ensuremath{\alpha}$ quartz to quartz II at $21\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ is irreversible. While quartz II is ferroelastic in principle, the transition itself is coelastic, as the shape of the newly formed crystal is determined by the handedness of $\ensuremath{\alpha}$-quartz. Upon releasing the pressure, our model quartz II remains stable down to $5\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, where it undergoes an isosymmetric transformation into a less dense polymorph. If the classical force field model of quartz II is compressed quickly to $50\phantom{\…
Comparison of two non-primitive methods for path integral simulations: Higher-order corrections vs. an effective propagator approach
Two methods are compared that are used in path integral simulations. Both methods aim to achieve faster convergence to the quantum limit than the so-called primitive algorithm (PA). One method, originally proposed by Takahashi and Imada, is based on a higher-order approximation (HOA) of the quantum mechanical density operator. The other method is based upon an effective propagator (EPr). This propagator is constructed such that it produces correctly one and two-particle imaginary time correlation functions in the limit of small densities even for finite Trotter numbers P. We discuss the conceptual differences between both methods and compare the convergence rate of both approaches. While th…
Quantum Creep and Quantum-Creep Transitions in 1D Sine-Gordon Chains
Discrete sine-Gordon (SG) chains are studied with path-integral molecular dynamics. Chains commensurate with the substrate show the transition from collective quantum creep to pinning at bead masses slightly larger than those predicted from the continuous SG model. Within the creep regime, a field-driven transition from creep to complete depinning is identified. The effects of disorder in the external potential on the chain's dynamics depend on the potential's roughness exponent $H$, i.e., quantum and classical fluctuations affect the current self-correlation functions differently for $H = 1/2$.
Elastic Constants of Quantum Solids by Path Integral Simulations
Two methods are proposed to evaluate the second-order elastic constants of quantum mechanically treated solids. One method is based on path-integral simulations in the (NVT) ensemble using an estimator for elastic constants. The other method is based on simulations in the (NpT) ensemble exploiting the relationship between strain fluctuations and elastic constants. The strengths and weaknesses of the methods are discussed thoroughly. We show how one can reduce statistical and systematic errors associated with so-called primitive estimators. The methods are then applied to solid argon at atmospheric pressures and solid helium 3 (hcp, fcc, and bcc) under varying pressures. Good agreement with …
Friction between Polymer Brushes in Good Solvent Conditions: Steady-State Sliding versus Transient Behavior
Previous molecular dynamics simulations of friction between polymer brushes in relative sliding motion [Kreer, T.; Muser, M. H.; Binder, K.; Klein, J. Langmuir 2001, 17, 7804] are extended beyond steady-state conditions. We study two different protocols: (i) stop and return and (ii) stop and go. In protocol (i), the relative, lateral motion between the two surfaces is stopped abruptly and reimposed opposite to the initial direction after the system could relax for some time. Protocol (ii) is similar except that the sliding direction is maintained. In the constant-velocity steady state, the average lateral extension lc of the polymers is found to be a power law of the sliding velocity v, na…
Conditions for static friction between flat crystalline surfaces
The conditions for the presence of static friction between two atomically smooth crystalline surfaces are investigated. Commensurate and incommensurate walls are studied. While two commensurate walls always pin at zero lateral force and positive pressures, incommensurate walls only pin if mobile atoms are present in the interface between the surfaces or if the solids are particularly soft. Surprisingly, static friction can be observed between rigid surfaces, either commensurate or incommensurate, that are separated by a freely diffusing fluid layer.
Computer simulations of a Lennard-Jones model for Ar1—x(N2)x: A prototype system for quadrupolar glasses
Abstract Recent theoretical studies of orientational ordering in pure and diluted nitrogen crystals are summarized. While pure N2 has a first order phase transition from a plastic crystal to a phase with long-range orientational order, dilution with argon atoms leads to a quadrupolar glass phase. Monte Carlo simulations are used to study these phases, considering also the behavior of isolated N2 impurities in Ar crystals. It is shown that a simple model that neglects electrostatic interactions and takes only Lennard-Jones interactions into account can describe already many properties in qualitative agreement with experiment. Even the slow dynamics of the quadrupole moments can be modeled by…
Many-body quantum dynamics by adiabatic path-integral molecular dynamics: Disordered Frenkel Kontorova models
The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent ), there is one regime in which the chain is pinned (large masses of chain particles) and one in which it is unpinned (small ). If the embedding potential can be classified as a random walk on large length scales ( ), then the chain is always pinned irrespective of the value of . For , two phonon-like branches appear in the spectra.
Computer Simulations of Undercooled Fluids and Glasses
An introduction to the Molecular Dynamics (MD) simulation of chemically realistic models for undercooled fluids and glasses is given, emphasizing silicatic materials such as molten silicon dioxide and its mixtures with sodium oxide and aluminium oxide, and comparing the simulation results to experimental data whenever possible.
Comparison of model potentials for molecular-dynamics simulations of silica.
Structural, thermomechanical, and dynamic properties of pure silica SiO2 are calculated with three different model potentials, namely, the potential suggested by van Beest, Kramer, and van Santen (BKS) [Phys. Rev. Lett. 64, 1955 (1990)], the fluctuating-charge potential with a Morse stretch term for the short-range interactions proposed by Demiralp, Cagin, and Goddard (DCG)[Phys. Rev. Lett. 82, 1708 (1999)], and a polarizable force field proposed by Tangney and Scandolo (TS) [J. Chem. Phys. 117, 8898 (2002)]. The DCG potential had to be modified due to flaws in the original treatment. While BKS reproduces many thermomechanical properties of different polymorphs rather accurately, it also sh…
Atomistic Simulations of Solid Friction
Friction between two solid bodies in relative sliding motion takes place on a large spectrum of length and time scales: From the nanometer/second scale in an atomic force microscope up to the extremely macroscopic scales of tectonic motion. Despite our familiarity with the effects of friction, fundamental questions remain unanswered. The atomistic origins of well-established phenomenological friction laws are controversial. Many explanations, seemingly well-established, have recently been called into question by new experimental results. Computer simulations have also revealed flaws in previous theoretical approaches and led to new insights into the atomistic processes responsible for frict…
Comment on “High-Pressure Elasticity ofα-Quartz: Instability and Ferroelastic Transition”
Piezoelectric coefficients by molecular dynamics simulations in the constant stress ensemble: A case study of quartz
Piezoelectric (strain) coefficients dij of quartz are calculated in terms of molecular dynamics as a function of pressure and temperature. We review the necessary formulas for the computation of electromechanical materials coefficients obtained at constant stress and temperature, and discuss how to overcome complications of the definition of polarization variations due to fluctuating box geometries. A method is employed suppressing significantly stochastic fluctuations of the estimators for piezoelectric coefficients. A recently suggested force field for the simulation of SiO2 reproduces available experimental data quite accurately. Predictions are made for the pressure dependence of dij of…
Frictional drag between polymer bearing surfaces
Some fundamental features of friction between two polymer bearing surfaces in relative sliding motion are investigated by molecular dynamics simulations. End-tethered and adsorbed polymers are considered under good and poor solvent conditions. The shear stress is measured while varying the solvent's viscosity, surface separation, degree of polymerization and grafting density. For all systems we observe shear thinning that is attributed to the orientation of the chains along the shear direction. This effect is particularly strong for brushes, for which the shear stress during the steady sliding state is mainly determined by the degree of overlap between the brushes.
Statistical Mechanics of Static and Low-Velocity Kinetic Friction
Average Structure vs. Real Structure: Molecular Dynamics Studies of Silica
The microscopic structure of a crystal and thermal fluctuations of the atoms constituting the crystal are intimately connected with the macroscopic elastic properties including mechanical stability. In some cases, however, the picture is more complex than that which is drawn in text books on solid state physics. (i) The instantaneous microscopic structure can deviate in a non-Gaussian way from the average structure even when domain disorder and/or crystal defects are absent. Quasi harmonic approximations may then turn out to be meaningless. (ii) The crystal is subject to external pressures that are sufficiently large in order to render the definition of elastic constants non unique. These t…
Simple Microscopic Theory of Amontons' Laws for Static Friction
A microscopic theory for the ubiquitous phenomenon of static friction is presented. Interactions between two surfaces are modeled by an energy penalty that increases exponentially with the degree of surface overlap. The resulting static friction is proportional to load, in accordance with Amontons' laws. However the friction coefficient between bare surfaces vanishes as the area of individual contacts grows, except in the rare case of commensurate surfaces. An area independent friction coefficient is obtained for any surface geometry when an adsorbed layer of mobile atoms is introduced between the surfaces. The predictions from our simple analytic model are confirmed by atomistically detail…
Frictional Drag Mechanisms between Polymer-Bearing Surfaces
The fundamental features of friction between two polymer-bearing surfaces in relative sliding motion are investigated by molecular dynamics simulation. Adsorbed and grafted polymers are considered in good and bad solutions. The solvent is not treated explicitly but indirectly in terms of a Langevin thermostat. In both systems, we observe shear thinning that is attributed to an orientation of the radius of gyration along the sliding direction. This effect is particularly strong for surfaces bearing polymer brushes. In this case, the shear stresses are mainly determined by the degree of the interpenetration of brushes.