Structural lubricity: Role of dimension and symmetry

When two chemically passivated solids are brought into contact, interfacial interactions between the solids compete with intrabulk elastic forces. The relative importance of these interactions, which are length-scale dependent, will be estimated using scaling arguments. If elastic interactions dominate on all length scales, solids will move as essentially rigid objects. This would imply superlow kinetic friction in UHV, provided wear was absent. The results of the scaling study depend on the symmetry of the surfaces and the dimensionalities of interface and solids. Some examples are discussed explicitly such as contacts between disordered three-dimensional solids and linear bearings realized from multiwall carbon nanotubes.Comment: 7 pages, 1 figur

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 the HOA method converges faster than the EPr approach, EPr gives surprisingly good estimates of thermal quantities already for P = 1. Despite a significant improvement with respect to PA, neither HOA nor EPr overcomes the need to increase P linearly with inverse temperature. We also derive the proper estimator for radial distribution functions for HOA based path integral simulations.Comment: 17 pages, latex, 6 postscript figure

Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals

We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation to this system. The one-particle orientational distribution function has a nontrivial dependence on the orientation and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids. We solve both equations for hard ellipsoids on a sc lattice. Compared to molecular liquids, the tensorial orientational correlators exhibit less structure. However, depending on the lengths a and b of the rotation axis and the perpendicular axes of the ellipsoids, different behavior is found. For oblate and prolate ellipsoids with b >= 0.35 (units of the lattice constant), damped oscillations in distinct directions of direct space occur for some correlators. They manifest themselves in some correlators in reciprocal space as a maximum at the Brillouin zone edge, accompanied by maxima at the zone center for other correlators. The oscillations indicate alternating orientational fluctuations, while the maxima at the zone center originate from nematic-like orientational fluctuations. For a <= 2.5 and b <= 0.35, the oscillations are weaker. For a >= 3.0 and b <= 0.35, no oscillations occur any longer. For many of the correlators in reciprocal space, an increase of a at fixed b leads to a divergence at the zone center q = 0, consistent with nematic-like long range fluctuations, and for some oblate and prolate systems with b ~< 1.0 a simultaneous tendency to divergence of few other correlators at the zone edge is observed. Comparison with correlators from MC simulations shows satisfactory agreement. We also obtain a phase boundary for order-disorder transitions.Comment: 20 pages, 13 figures, submitted to Phys. Rev.

Hybrid atomistic-coarse-grained treatment of thin-film lubrication. I

A technique that melds an atomistic description of the interfacial region with a coarse-grained description of the far regions of the solid substrates is presented and applied to a two-dimensional model contact consisting of planar solid substrates separated by a monolayer fluid film. The hybrid method yields results in excellent agreement with the “exact” (i.e., fully atomistic) results. The importance of a proper accounting for the elastic response of the substrates, which is reliably and efficiently accomplished through coarse-graining of the far regions, is demonstrated

Portable implementation of a quantum thermal bath for molecular dynamics simulations

Recently, Dammak and coworkers (H. Dammak, Y. Chalopin, M. Laroche, M. Hayoun, and J.J. Greffet. Quantumthermal bath for molecular dynamics simulation. Phys. Rev. Lett., 103:190601, 2009.) proposed that the quantum statistics of vibrations in condensed systems at low temperature could be simulated by running molecular dynamics simulations in the presence of a colored noise with an appropriate power spectral density. In the present contribution, we show how this method can be implemented in a flexible manner and at a low computational cost by synthesizing the corresponding noise 'on the fly'. The proposed algorithm is tested for a simple harmonic chain as well as for a more realistic model of aluminium crystal. The energy and Debye-Waller factor are shown to be in good agreement with those obtained from harmonic approximations based on the phonon spectrum of the systems. The limitations of the method associated with anharmonic effects are also briefly discussed. Some perspectives for disordered materials and heat transfer are considered.Comment: Accepted for publication in Journal of Statistical Physic

Friction Laws for Elastic Nano-Scale Contacts

The effect of surface curvature on the law relating frictional forces F with normal load L is investigated by molecular dynamics simulations as a function of surface symmetry, adhesion, and contamination. Curved, non-adhering, dry, commensurate surfaces show a linear dependency, F proportional to L, similar to dry flat commensurate or amorphous surfaces and macroscopic surfaces. In contrast, curved, non-adhering, dry, amorphous surfaces show F proportional to L^(2/3) similar to friction force microscopes. In our model, adhesive effects are most adequately described by the Hertz plus offset model, as the simulations are confined to small contact radii. Curved lubricated or contaminated surfaces show again different behavior; details depend on how much of the contaminant gets squeezed out of the contact. Also, it is seen that the friction force in the lubricated case is mainly due to atoms at the entrance of the tip.Comment: 7 pages, 5 figures, submitted to Europhys. Let

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 available experimental data on elastic constants is found for helium 3. Predictions are made for the thermal expectation value of the kinetic energy of solid helium 3.Comment: 9 pages doublecolumn, 6 figures, submitted to PR