Martin H. Müser

Simple microscopic theory of Amontons's 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 Amontonss 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 detailed molecular dynamics simulations.

Transverse and normal interfacial stiffness of solids with randomly rough surfaces

Using a theoretical approach and computer simulations, we calculate the normal stiffness K(perpendicular) and the transverse stiffness K(parallel) of the interface between two contacting isotropic solids with randomly rough surfaces and Poisson ratio ν. The theoretical predictions for K(perpendicular) agree well with the simulations. Moreover, the theoretical result for the ratio K(perpendicular)/K(parallel) is (2 - ν)/(2 - 2ν), as predicted by Mindlin for a single circular contact region. Finally, we compare the theory to experimental ultrasonic data.

A generalization of the charge equilibration method for nonmetallic materials.

Assigning effective atomic charges that properly reproduce the electrostatic fields of molecules is a crucial step in the construction of accurate interatomic potentials. We propose a new approach to calculate these charges, which as previous approaches are, is based on the idea of charge equilibration. However, we only allow charge to flow between covalently bonded neighbors by using the concept of so-called split charges. The semiempirical fit parameters in our approach do not only reflect atomic properties (electronegativity and atomic hardness) but also bond-dependent properties. The new method contains two popular but hitherto disjunct approaches as limiting cases. We apply our methodology to a set of molecules containing the elements silicon, carbon, oxygen, and hydrogen. Effective charges derived from electrostatic potential surfaces can be predicted more than twice as accurately as with previous works, at the expense of one additional fit parameter per bond type controlling the polarizability between two bonded atoms. Additional bond-type parameters can be introduced, but barely improve the results. An increase in accuracy of only 30% over existing techniques is achieved when predicting Mulliken charges. However, this could be improved with additional bond-type parameters.

Path integral simulations of rotors : theory and applications

An outline of numerical path integral techniques which allows one to treat the rotational component of molecular motion is given in a unified framework. Special attention is paid to the particular aspects of this treatment depending on the dimension of the subspace for rotations, which leads to optimized methods for one-, two- and three-dimensional rigid rotors. The implications of the coupling between rotational and nuclear spin degrees of freedom, due to the symmetry requirement of the total wave function under exchange of identical particles, are discussed. Several recent applications of path integral simulations of rigid rotors are presented. These examples include both strongly simplified and very realistic models for investigating the properties of molecular impurities and clusters, rotors physisorbed on surfaces, and condensed molecular phases. Where available, the results of approximate calculations based on quasi-classical, quasi-harmonic and mean-field theories are compared to the path integral simulations.

Elastic contact between self-affine surfaces: comparison of numerical stress and contact correlation functions with analytic predictions

Contact between an elastic manifold and a rigid substrate with a self-affine fractal surface is reinvestigated with Greens function molecular dynamics. The Fourier transforms of the stress and contact autocorrelation functions are found to decrease as |q|?? where q is the wavevector. Upper and lower bounds on the ratio of the two correlation functions are used to argue that they have the same scaling exponent ?. Analysis of numerical results gives ? = 1+H, where H is the Hurst roughness exponent. This is consistent with Perssons contact mechanics theory, while asperity models give ? = 2(1+H). The effect of increasing the range of interactions from a hard sphere repulsion to exponential decay is analyzed. Results for exponential interactions are accurately described by recent systematic corrections to Perssons theory. The relation between the area of simply connected contact patches and the normal force is also studied. Below a threshold size the contact area and force are consistent with Hertzian contact mechanics, while area and force are linearly related in larger contact patches.

Contact mechanics of real vs. randomly rough surfaces: A Green's function molecular dynamics study

It is commonly assumed that knowing the height auto-correlation function of two solids in contact along with their materials properties is sufficient to predict the contact pressure distribution P(p). We investigate this assumption with contact mechanics calculations that are based on quickly converging Greens function molecular dynamics. In our simulations, elastically deformable solids are pressed against a rigid substrate. Their profile is either given by experimental data or produced with random numbers such that the artificially generated height spectra ressemble that of the real profiles. Randomly rough surfaces produce Gaussian tails in the P(p)s, while they are exponential for experimentally determined topographies. This difference, however, does not affect significantly the true contact area, which, for the given real profile is about 20% larger than that of the random surface. Both surfaces obey Perssons contact mechanics theory reasonably well.

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 Perssons contact mechanics theory with a slightly modified version of Bruggemans effective-medium solution of the Reynolds equation.

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 threedimensional solids and linear bearings realized from multiwall carbon nanotubes. Introduction. – Many small-scale devices cannot be miniaturized further, because friction and wear appear to be exceedingly large in nanoscale machines. This limitation seems to arise, because the surface to volume ratio is large in small systems and thus surface forces such as friction become relatively large. However, many theoretical studies [1, 2, 3, 4, 5] and most recently an increasing number of experiments [6, 7, 8, 9, 10, 11] indicate that shear forces can be tremendously small between two atomically flat surfaces. These findings spur the hope for new avenues to reduce friction in nano-scale applications. Superlow friction was first suggested by Hirano and Shinjo [1, 2]. Their calculations indicated that no instabilities occur when two atomically smooth copper solids slide past each other provided that they are sufficiently misaligned. The absence of instabilities in such contacts implies that kinetic friction approaches zero at infinitely small velocities, even when thermal fluctuations are absent. Hirano and Shinjo called such superlow friction superlubricity. This term is often considered unfortunate, because one may expect zero friction in the sliding state in analogy to superconductivity and superfluidity. However, due to the emission of sound waves, which also occur when instabilities are absent, a drag force linear in velocity will persist. It might therefore be more appropriate to call the effect structural lubricity, as the low friction arises from the structural incompatibility of the two contacting solids rather than from a Bose Einstein condensate of bosons. The main reason for the low friction is that lateral forces between two non-matching, rigid solids cancel systematically for incommensurate interfaces and stochastically between disordered surfaces, so that the average force per unit area decreases quickly with increasing contact area.

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.

Friction laws for elastic nanoscale 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 dependence, F L, similar to dry flat commensurate or amorphous surfaces and macroscopic surfaces. In contrast, curved, non-adhering, dry, amorphous surfaces show F L2/3 similar to friction force microscopes. Curved lubricated or contaminated surfaces show again different behaviour; details depend on how much of the contaminant gets squeezed out of the contact. The shear stress distribution in the contact is highly non-uniform in all cases, i.e. it is seen that the friction force in the lubricated case is mainly due to atoms at the entrance of the tip.