Astrid S. de Wijn

The effect of temperature and velocity on superlubricity

We study the effects of temperature and sliding velocity on superlubricity in numerical simulations of the Frenkel-Kontorova model. We show that resonant excitations of the phonons in an incommensurate sliding body lead to an effective friction and to thermal equilibrium with energy distributed over the internal degrees of freedom. For finite temperature, the effective friction can be described well in terms of a viscous damping force, with a damping coefficient that emerges naturally from the microscopic dynamics. This damping coefficient is a non-monotonic function of the sliding velocity which peaks around resonant velocities and increases with temperature. At low velocities, it remains finite and nonzero, indicating the preservation of superlubricity in the zero-velocity limit. Finally, we propose experimental systems in which our results could be verified.

Collective superlubricity of graphene flakes

We investigate solid lubrication of graphene and graphene flakes using atomistic molecular-dynamics simulations. We find that graphene flakes yield lower friction than graphene as a result of a collective mechanism that emerges from the independent behaviour of the flakes. By freezing out different degrees of freedom of the flakes, we are able to attribute the low friction to non-simultaneous slipping of the individual flakes. We also compare the results of the atomistic simulations to those of a simplified two-dimensional model and find that the behaviour of the latter is strongly dependent on parameters, which emerge naturally from the atomistic simulations.

Relating chaos to deterministic diffusion of a molecule adsorbed on a surface

Chaotic internal degrees of freedom of a molecule can act as noise and affect the diffusion of the molecule on a substrate. A separation of timescales between the fast internal dynamics and the slow motion of the centre of mass on the substrate makes it possible to directly link chaos to diffusion. We discuss the conditions under which this is possible, and show that in simple atomistic models with pair-wise harmonic potentials, strong chaos can arise through the geometry. Using molecular dynamics simulations, we demonstrate that a realistic model of benzene is indeed chaotic, and that the internal chaos affects the diffusion on a graphite substrate.

Numerical aspects of real-space approaches to strong-field electron dynamics

Abstract Numerical methods for calculating strong-field, nonperturbative electron dynamics are investigated. Two different quantum–mechanical approaches are discussed: the time-dependent Schrodinger equation and time-dependent density functional theory. We show that when solving the time-dependent Schrodinger equation, small errors in the initial ground-state wave function can be magnified considerably during propagation. A scheme is presented to efficiently obtain the ground state with high accuracy. We further demonstrate that the commonly-used absorbing boundary conditions can severely influence the results. The requirements on the boundary conditions are somewhat less stringent in effective single-particle approaches such as time-dependent density functional theory. We point out how results from accurate wave-function based calculations can be used to improve the density functional description of long-ranged, nonlinear electron dynamics. We present details of a method to reconstruct, numerically, the full, unapproximated, Kohn–Sham potential from the density and current of the exact system.

Emergent friction in two-dimensional Frenkel-Kontorova models

Simple models for friction are typically one-dimensional, but real interfaces are two-dimensional. We investigate the effects of the second dimension on static and dynamic friction by using the Frenkel-Kontorova (FK) model. We study the two most straightforward extensions of the FK model to two dimensions and simulate both the static and dynamic properties. We show that the behavior of the static friction is robust and remains similar in two dimensions for physically reasonable parameter values. The dynamic friction, however, is strongly influenced by the second dimension and the accompanying additional dynamics and parameters introduced into the models. We discuss our results in terms of the thermal equilibration and phonon dispersion relations of the lattices, establishing a physically realistic and suitable two-dimensional extension of the FK model. We find that the presence of additional dissipation channels can increase the friction and produces significantly different temperature dependence when compared to the one-dimensional case. We also briefly study the anisotropy of the dynamic friction and show highly nontrivial effects, including that the friction anisotropy can lead to motion in different directions depending on the value of the initial velocity.

Stability of Low-Friction Surface Sliding of Nanocrystals with Rectangular Symmetry and Application to W on NaF(001)

We investigate the stability of low-friction sliding of nanocrystal with rectangular atomic arrangement on rectangular lattices, for which analytical results can be obtained. We find that several incommensurate periodic orbits exist and are stable against thermal fluctuations and other perturbations. As incommensurate orientations lead to low corrugation, and therefore low friction, such incommensurate periodic orbits are interesting for the study of nanotribology. The analytical results compare very well with simulations of W nanocrystals on NaF(001). The geometry and high typical corrugation of substrates with square lattices increase the robustness when compared to typical hexagonal lattices, such as graphite.

Preface to the special section on nano- and mesoscale friction

Recent widespread efforts to characterize the mechanisms of friction in micrometric structures (mesoscale) down to the size range of atoms and molecules (nanoscale) allow us to come closer to the ultimate goal of improving our control of friction, adhesion and wear by design. The potential impact of this interdisciplinary research, known as nanotribology, on technology and everyday life is widespread, with key applications in industrial safety, energy and materials efficiency, and more generally sustainable development and economics. Europe has a very strong research community in nanoscale friction, which encompasses physics, materials science, chemistry, earth and life sciences, with excellent links between academic and industrial actors. The network of researchers has been expanding rapidly in the past few years, and this special section highlights some of the work developed in this community.

A radius of curvature approach to the Kolmogorov–Sinai entropy of dilute hard particles in equilibrium

We consider the Kolmogorov–Sinai entropy for dilute gases of N hard disks or spheres. This can be expanded in density as , with a the diameter of the sphere or disk, n the density, and d the dimensionality of the system. We estimate the constant B by solving a linear differential equation for the approximate distribution of eigenvalues of the inverse radius of curvature tensor. We compare the resulting values of B both to previous estimates and to existing simulation results, finding very good agreement with the latter. Also, we compare the distribution of eigenvalues of the inverse radius of curvature tensor resulting from our calculations to new simulation results. For most of the spectrum the agreement between our calculations and the simulations again is very good.