222 research outputs found
Towards time-dependent, non-equilibrium charge-transfer force fields: Contact electrification and history-dependent dissociation limits
Force fields uniquely assign interatomic forces for a given set of atomic
coordinates. The underlying assumption is that electrons are in their
quantum-mechanical ground state or in thermal equilibrium. However, there is an
abundance of cases where this is unjustified because the system is only locally
in equilibrium. In particular, the fractional charges of atoms, clusters, or
solids tend to not only depend on atomic positions but also on how the system
reached its state. For example, the charge of an isolated solid -- and thus the
forces between atoms in that solid -- usually depends on the counterbody with
which it has last formed contact. Similarly, the charge of an atom, resulting
from the dissociation of a molecule, can differ for different solvents in which
the dissociation took place. In this paper we demonstrate that such
charge-transfer history effects can be accounted for by assigning discrete
oxidation states to atoms. With our method, an atom can donate an integer
charge to another, nearby atom to change its oxidation state as in a redox
reaction. In addition to integer charges, atoms can exchange "partial charges"
which are determined with the split charge equilibration method.Comment: 11 pages, 7 figure
Contact mechanics of and Reynolds flow through saddle points: On the coalescence of contact patches and the leakage rate through near-critical constrictions
We study numerically local models for the mechanical contact between two
solids with rough surfaces. When the solids softly touch either through
adhesion or by a small normal load , contact only forms at isolated patches
and fluids can pass through the interface. When the load surpasses a threshold
value, , adjacent patches coalesce at a critical constriction, i.e., near
points where the interfacial separation between the undeformed surfaces forms a
saddle point. This process is continuous without adhesion and the interfacial
separation near percolation is fully defined by scaling factors and the sign of
. The scaling factors lead to a Reynolds flow resistance which diverges
as with . Contact merging and destruction near
saddle points becomes discontinuous when either short-range adhesion or
specific short-range repulsion are added to the hard-wall repulsion. These
results imply that coalescence and break-up of contact patches can contribute
to Coulomb friction and contact aging.Comment: 6 pages, 6 figures, submitted to Euro. Phys. Let
Shear Thinning in the Prandtl Model and Its Relation to Generalized Newtonian Fluids
The Prandtl model is certainly the simplest and most generic microscopic model describing
solid friction. It consists of a single, thermalized atom attached to a spring, which is dragged past
a sinusoidal potential representing the surface energy corrugation of a counterface. While it was
primarily introduced to rationalize how Coulomb’s friction law can arise from small-scale instabilities,
Prandtl argued that his model also describes the shear thinning of liquids. Given its success regarding
the interpretation of atomic-force-microscopy experiments, surprisingly little attention has been
paid to the question how the Prandtl model relates to fluid rheology. Analyzing its Langevin and
Brownian dynamics, we show that the Prandtl model produces friction–velocity relationships, which,
converted to a dependence of effective (excess) viscosity on shear rate η(γ˙), is strikingly similar
to the Carreau–Yasuda (CY) relation, which is obeyed by many non-Newtonian liquids. The two
dimensionless parameters in the CY relation are found to span a broad range of values. When
thermal energy is small compared to the corrugation of the sinusoidal potential, the leading-order γ˙
2
corrections to the equilibrium viscosity only matter in the initial part of the cross-over from Stokes
friction to the regime, where η obeys approximately a sublinear power law of 1/γ
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. This contrasts with the behavior of essentially classical
systems like xenon, where the effective potential is independent of
temperature. It is conjectured that, owing to this difference in behavior
between classical and quantum-mechanical systems, the crossover behavior
observed for helium in the vicinity of the critical point differs qualitatively
from that of other simple liquids
Systematic analysis of Persson's contact mechanics theory of randomly rough elastic surfaces
We systematically check explicit and implicit assumptions of Persson's
contact mechanics theory. It casts the evolution of the pressure distribution
with increasing resolution of surface roughness as a diffusive
process, in which resolution plays the role of time. The tested key assumptions
of the theory are: (a) the diffusion coefficient is independent of pressure
, (b) the diffusion process is drift-free at any value of , (c) the point
acts as an absorbing barrier, i.e., once a point falls out of contact, it
never reenters again, (d) the Fourier component of the elastic energy is only
populated if the appropriate wave vector is resolved, and (e) it no longer
changes when even smaller wavelengths are resolved. Using high-resolution
numerical simulations, we quantify deviations from these approximations and
find quite significant discrepancies in some cases. For example, the drift
becomes substantial for small values of , which typically represent points
in real space close to a contact line. On the other hand, there is a
significant flux of points reentering contact. These and other identified
deviations cancel each other to a large degree, resulting in an overall
excellent description for contact area, contact geometry, and gap distribution
functions. Similar fortuitous error cancellations cannot be guaranteed under
different circumstances, for instance when investigating rubber friction. The
results of the simulations may provide guidelines for a systematic improvement
of the theory.Comment: 27 pages, 16 figures, accepted for publication by Journal of Physics:
Condensed Matte
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