50 research outputs found
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 compared to typical
hexagonal lattices, such as graphite
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.Comment: 14 pages, 13 figure
Shear viscosity of pseudo hard-spheres
We present molecular dynamics simulations of pseudo hard sphere fluid
(generalized WCA potential with exponents (50, 49) proposed by Jover et al. J.
Chem. Phys 137, (2012)) using GROMACS package. The equation of state and radial
distribution functions at contact are obtained from simulations and compared to
the available theory of true hard spheres (HS) and available data on pseudo
hard spheres. The comparison shows agreements with data by Jover et al. and the
Carnahan-Starling equation of HS. The shear viscosity is obtained from the
simulations and compared to the Enskog expression and previous HS simulations.
It is demonstrated that the PHS potential reproduces the HS shear viscosity
accurately.Comment: 7 figure
Understanding the friction of atomically thin layered materials
Friction is a ubiquitous phenomenon that greatly affects our everyday lives
and is responsible for large amounts of energy loss in industrialised
societies. Layered materials such as graphene have interesting frictional
properties and are often used as (additives to) lubricants to reduce friction
and protect against wear. Experimental Atomic Force Microscopy studies and
detailed simulations have shown a number of intriguing effects such as friction
strengthening and dependence of friction on the number of layers covering a
surface. Here, we propose a simple, fundamental, model for friction on thin
sheets. We use our model to explain a variety of seemingly contradictory
experimental as well as numerical results. This model can serve as a basis for
understanding friction on thin sheets, and opens up new possibilities for
ultimately controlling their friction and wear protection.Comment: 8 pages, 6 figures, publication pendin
Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov
exponents of small absolute value exhibit interesting characteristics leading
to speculations about connections to non-equilibrium statistical mechanics.
Analytical approaches to these exponents so far can be divided into two groups,
macroscopically oriented approaches, using kinetic theory or hydrodynamics, and
more microscopically oriented random-matrix approaches in quasi-one-dimensional
systems. In this paper, I present an approach using random matrices and weak
disorder expansion in an arbitrary number of dimensions. Correlations between
subsequent collisions of a particle are taken into account. It is shown that
the results are identical to those of a previous approach based on an extended
Enskog-equation. I conclude that each approach has its merits, and provides
different insights into the approximations made, which include the
Sto{\ss}zahlansatz, the continuum limit, and the long-wavelength approximation.
The comparison also gives insight into possible connections between Lyapunov
exponents and fluctuations
Imaging high-speed friction at the nanometer scale
Friction is a complicated phenomenon involving nonlinear dynamics at
different length and time scales[1, 2]. The microscopic origin of friction is
poorly understood, due in part to a lack of methods for measuring the force on
a nanometer-scale asperity sliding at velocity of the order of cm/s.[3, 4]
Despite enormous advance in experimental techniques[5], this combination of
small length scale and high velocity remained illusive. Here we present a
technique for rapidly measuring the frictional forces on a single asperity (an
AFM tip) over a velocity range from zero to several cm/s. At each image pixel
we obtain the velocity dependence of both conservative and dissipative forces,
revealing the transition from stick-slip to a smooth sliding friction[1, 6]. We
explain measurements on graphite using a modified Prandtl-Tomlinson model that
takes into account the damped elastic deformation of the asperity. With its
greatly improved force sensitivity and very small sliding amplitude, our method
enables rapid and detailed surface mapping of the full velocity-dependence of
frictional forces with less than 10~nm spatial resolution.Comment: 7 pages, 4 figure