Locked-to-running transition in the two-dimensional underdamped driven Frenkel-Kontorova model

Kink propagation and solute partitioning in an atomic monolayer on a substrate

When a monolayer of Lennard-Jones atoms is driven by an external force over an atomically spaced lattice, the atoms do not move in the direction of the force. By considering monolayers containing a solvent and two different solutes, we show that the different atomic species follow distinct directions and so partition from one another and from the solvent. The strength of the driving force is chosen so that at any instant, most atoms are stationary while only a small fraction propagates as solitary waves. In this regime, the mean velocity of the layer is due to the nonzero contribution from merely a few atoms. We also present a simple theory, based on the probability that an atom in the monolayer will hop from one equilibrium location to the next, that explains the distinct directions of atomic migration.

Friction and nonlinear dynamics

The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental techniques and computational resources has stimulated the development of more refined and accurate mathematical and numerical models, capable of capturing many of the essentially nonlinear phenomena involved in friction.

Dynamical phases of attractive particles sliding on a structured surface

Inspired by experiments on quartz crystal microbalance setups, we study the mobility of a monolayer of Lennard-Jones particles driven over a hexagonal external potential. We pay special attention to the changes in the dynamical phases that arise when the lattice constant of the external substrate potential and the Lennard-Jones interaction are mismatched. We find that if the average particle separation is such that the particles repel each other, or interact harmonically, the qualitative behavior of the system is akin to that of a monolayer of purely repulsive Yukawa particles. On the other hand, if the particles typically attract each other, the ensuing dynamical states are determined entirely by the relative strength of the Lennard-Jones interaction with respect to that of the external potential.

Frictional dynamics of stiff monolayers: from nucleation dynamics to thermal sliding

The inherently nonlinear dynamics of two surfaces as they are driven past each other, a phenomenon known as dry friction, has yet to be fully understood on an atomistic level. New experiments on colloidal monolayers forced over laser-generated substrates now offer the opportunity to investigate friction with single-particle resolution. Here, we use analytical theory and computer simulations to study the effect of thermal fluctuations on the stick-slip mechanism characteristic for the frictional response of a stiff colloidal monolayer on a commensurate substrate. By performing a harmonic expansion of the energy and employing elementary statistical mechanics, we map the motion of the monolayer onto a simple differential equation. Analytical expressions derived from our approach predict a transition from nucleation dynamics, where the monolayer moves in a sequence of activated hops over energy barriers, to "thermal sliding", in which the effective substrate barrier opposing the motion of the monolayer disappears due to thermal fluctuations, leading to continuous, uninterrupted sliding motion. Furthermore, we find that the average velocity of the monolayer for large driving forces obeys a simple scaling behavior that is consistent with the existence of a static friction. For small forces, however, nucleation provides a mode of motion that leads to a small but non-vanishing mobility of the monolayer. Data obtained from simulations confirm this picture and agree quantitatively with our analytical formulae. The theory developed here holds under general conditions for sufficiently strong inter-particle repulsions and it yields specific predictions that can be tested in experiments.

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

We numerically examine colloidal particles driven over a muffin tin substrate. Previous studies of this model identified a variety of commensurate and incommensurate static phases in which topological defects can form domain walls, ordered stripes, superlattices, or disordered patchy regimes as a function of the filling fraction. Here, we show that the addition of an external drive to these static phases can produce distinct dynamical responses. At incommensurate fillings the flow occurs in the form of localized pulses or solitons correlated with topological defect structures. Transitions between different modes of motion can occur as a function of increasing drive. We measure the average particle velocity for specific ranges of external drive and show that changes in the velocity response correlate with changes in the topological defect arrangements. We also demonstrate that in the different dynamic phases, the particles have distinct trajectories and velocity distributions. Dynamic transitions between ordered and disordered flows exhibit hysteresis, while in strongly disordered regimes there is no hysteresis and the velocity-force curves are smooth. When stripe patterns are present, transport can occur at an angle to the driving direction.

Static and dynamic friction in sliding colloidal monolayers

In a pioneer experiment, Bohlein et al. realized the controlled sliding of two-dimensional colloidal crystals over laser-generated periodic or quasi-periodic potentials. Here we present realistic simulations and arguments that besides reproducing the main experimentally observed features give a first theoretical demonstration of the potential impact of colloid sliding in nanotribology. The free motion of solitons and antisolitons in the sliding of hard incommensurate crystals is contrasted with the soliton-antisoliton pair nucleation at the large static friction threshold F(s) when the two lattices are commensurate and pinned. The frictional work directly extracted from particles' velocities can be analyzed as a function of classic tribological parameters, including speed, spacing, and amplitude of the periodic potential (representing, respectively, the mismatch of the sliding interface and the corrugation, or "load"). These and other features suggestive of further experiments and insights promote colloid sliding to a unique friction study instrument.

Observation of kinks and antikinks in colloidal monolayers driven across ordered surfaces

Friction between solids is responsible for many phenomena such as earthquakes, wear or crack propagation. Unlike macroscopic objects, which only touch locally owing to their surface roughness, spatially extended contacts form between atomically flat surfaces. They are described by the Frenkel-Kontorova model, which considers a monolayer of interacting particles on a periodic substrate potential. In addition to the well-known stick-slip motion, such models also predict the formation of kinks and antikinks, which greatly reduce the friction between the monolayer and the substrate. Here, we report the direct observation of kinks and antikinks in a two-dimensional colloidal crystal that is driven across different types of ordered substrate. We show that the frictional properties only depend on the number and density of such excitations, which propagate through the monolayer along the direction of the applied force. In addition, we also observe kinks on quasicrystalline surfaces, which demonstrates that they are not limited to periodic substrates but occur under more general conditions.

Onset of frictional slip by domain nucleation in adsorbed monolayers

It has been known for centuries that a body in contact with a substrate will start to slide when the lateral force exceeds the static friction force. Yet the microscopic mechanisms ruling the crossover from static to dynamic friction are still the object of active research. Here, we analyze the onset of slip of a xenon (Xe) monolayer sliding on a copper (Cu) substrate. We consider thermal-activated creep under a small external lateral force, and observe that slip proceeds by the nucleation and growth of domains in the commensurate interface between the film and the substrate. We measure the activation energy for the nucleation process considering its dependence on the external force, the substrate corrugation, and particle interactions in the film. To understand the results, we use the classical theory of nucleation and compute analytically the activation energy which turns out to be in excellent agreement with numerical results. We discuss the relevance of our results to understand experiments on the sliding of adsorbed monolayers.

Dynamic phases in the two-dimensional underdamped driven Frenkel-Kontorova model

We study the nonlinear dc response of a two-dimensional underdamped system of interacting atoms subject to an isotropic periodic external potential with triangular symmetry. When driving force increases, the system transfers from a disorder locked state to an ordered sliding state corresponding to a moving crystal. By varying the values of the effective elastic constant, damping, and temperature, we found different scenarios and intermediate phases during the ordering transition. For a soft atomic layer, the system passes through a plastic-channel regime that appears as a steady-state regime at higher values of the damping coefficient. For high values of the effective elastic constant, when the atomic layer is stiff, the intermediate plastic phase corresponds to a traffic-jam regime with immobile islands in the sea of running atoms. At a high driving of the stiff layer, a solitonlike elastic flow of atoms has been observed.