Nanoscopic friction under electrochemical control.

We propose a theoretical model of friction under electrochemical conditions focusing on the interaction of a force microscope tip with adsorbed polar molecules whose orientation depends on the applied electric field. We demonstrate that the dependence of friction force on the electric field is determined by the interplay of two channels of energy dissipation: (i) the rotation of dipoles and (ii) slips of the tip over potential barriers. We suggest a promising strategy to achieve a strong dependence of nanoscopic friction on the external field based on the competition between long-range electrostatic interactions and short-range chemical interactions between tip and adsorbed polar molecules.

Voltage-dependent capacitance of metallic nanoparticles at a liquid/liquid interface.

A theoretical model is described for the voltage-dependent capacitance across the interface between two immiscible electrolytic solutions that is partially or completely covered with nanoparticles. The model is based on the description of competitive contributions of electrical double layers at the free interface and around nanoparticles. The effect of different system parameters is rationalised, and theoretical predictions are shown to be in agreement with available experimental data. The model provides a route for the characterisation of nanoparticle layers at liquid/liquid interfaces using capacitance measurements.

Formation and rupture of capillary bridges in atomic scale friction.

While formation of capillary bridges significantly contributes to the adhesion and friction at micro- and nanoscales, many key aspects of dynamics of capillary condensation and its effect on friction forces are still not well understood. Here, by analytical model and numerical simulations, we address the origin of reduction of friction force with velocity and increase of friction with temperature, which have been experimentally observed under humid ambient conditions. These observations differ significantly from the results of friction experiments carried out under ultrahigh vacuum, and disagree with predictions of thermal Prandtl-Tomlinson model of friction. Our calculations demonstrate what information on the kinetics of capillary condensation can be extracted from measurements of friction forces and suggest optimal conditions for obtaining this information.

Giant Stark effect in quantum dots at liquid/liquid interfaces: a new option for tunable optical filters.

Control of the fundamental absorption edge of a quantum dot with an applied electric field has been limited by the breakdown fields of the solid-state material surrounding the dot. However, much larger fields can be applied at the interface of two immiscible electrolytic solutions (ITIES) in an electrochemical cell. These electric fields also localize the quantum dots at the ITIES. Our analysis shows that semiconductor nanocrystals localized at the ITIES should have electric-field-tunable optical properties across much of the visible spectrum. The transparency of the liquids in such cells indicates that this configuration would be well suited for electrically tunable optical filters with wide-angle acceptance.

Interfacial ferroelectricity by van der Waals sliding.

Despite their partial ionic nature, many layered diatomic crystals avoid internal electric polarization by forming a centrosymmetric lattice at their optimal van-der-Waals stacking. Here, we report a stable ferroelectric order emerging at the interface between two naturally-grown flakes of hexagonal-boron-nitride, which are stacked together in a metastable non-centrosymmetric parallel orientation. We observe alternating domains of inverted normal polarization, caused by a lateral shift of one lattice site between the domains. Reversible polarization switching coupled to lateral sliding is achieved by scanning a biased tip above the surface. Our calculations trace the origin of the phenomenon to a subtle interplay between charge redistribution and ionic displacement, and provide intuitive insights to explore the interfacial polarization and its unique "slidetronics" switching mechanism.

Dynamics of transition from static to kinetic friction.

We propose a model for a description of dynamics of cracklike processes that occur at the interface between two blocks prior to the onset of frictional motion. We find that the onset of sliding is preceded by well-defined detachment fronts initiated at the slider trailing edge and extended across the slider over limited lengths smaller than the overall length of the slider. Three different types of detachment fronts may play a role in the onset of sliding: (i) Rayleigh (surface sound) fronts, (ii) slow detachment fronts, and (iii) fast fronts. The important consequence of the precursor dynamics is that before the transition to overall sliding occurs, the initially uniform, unstressed slider is already transformed into a highly nonuniform, stressed state. Our model allows us to explain experimental observations and predicts the effect of material properties on the dynamics of the transition to sliding.

Single-molecule pulling experiments: when the stiffness of the pulling device matters.

Using Langevin modeling, we investigate the role of the experimental setup on the unbinding forces measured in single-molecule pulling experiments. We demonstrate that the stiffness of the pulling device, K(eff), may influence the unbinding forces through its effect on the barrier heights for both unbinding and rebinding processes. Under realistic conditions the effect of K(eff) on the rebinding barrier is shown to play the most important role. This results in a significant increase of the mean unbinding force with the stiffness for a given loading rate. Thus, in contrast to the phenomenological Bell model, we find that the loading rate (the multiplicative value K(eff)V, V being the pulling velocity) is not the only control parameter that determines the mean unbinding force. If interested in intrinsic properties of a molecular system, we recommend probing the system in the parameter range corresponding to a weak spring and relatively high loading rates where rebinding is negligible.

Controlling microscopic friction through mechanical oscillations.

We study in detail the recent suggestions by Tshiprut [Phys. Rev. Lett. 95, 016101 (2005)] to tune tribological properties at the nanoscale by subjecting a substrate to periodic mechanical oscillations. We show that both in stick-slip and sliding regimes of motion friction can be tuned and reduced by controlling the frequency and amplitude of the imposed substrate lateral excitations. We demonstrate that the mechanisms of oscillation-induced reduction of friction are different for stick-slip and sliding dynamics. In the first regime the effect results from a giant enhancement of surface diffusion, while in the second regime it is due to the interplay between washboard and oscillation frequencies that leads to the occurrence of parametric resonances. Moreover, we show that for a particular set of parameters it is possible to sustain the motion with only the oscillations.

Sliding friction of graphene/hexagonal -boron nitride heterojunctions: a route to robust superlubricity.

The origin of ultra-low friction exhibited by heterogeneous junctions of graphene and hexagonal boron nitride (h-BN) is revealed. For aligned interfaces, we identify a characteristic contact size, below which the junction behaves like its homogeneous counterparts with friction forces that grow linearly with the contact area. Superlubricity sets in due to the progressive appearance of Moiré patterns resulting in a collective stick-slip motion of the elevated super-structure ridges that turns into smooth soliton-like gliding with increasing contact size. Incommensurability effects are enhanced in misaligned contacts, where the friction coefficients further drop by orders of magnitude. Our fully atomistic simulations show that the superlubric regime in graphene/h-BN heterostructures persists up to significantly higher loads compared to the well-studied twisted homogeneous graphene interface. This indicates the potential of achieving robust superlubricity in practical applications using two-dimensional layered materials heterojunctions.

Dependence of the Enzymatic Velocity on the Substrate Dissociation Rate.

Enzymes are biological catalysts that play a fundamental role in all living systems by supporting the selectivity and the speed for almost all cellular processes. While the general principles of enzyme functioning are known, the specific details of how they work at the microscopic level are not always available. Simple Michaelis-Menten kinetics assumes that the enzyme-substrate complex has only one conformation that decays as a single exponential. As a consequence, the enzymatic velocity decreases as the dissociation (off) rate constant of the complex increases. Recently, Reuveni et al. [ Proc. Natl. Acad. Sci. USA 2014 , 111 , 4391 - 4396 ] showed that it is possible for the enzymatic velocity to increase when the off rate becomes higher, if the enzyme-substrate complex has many conformations which dissociate with the same off rate constant. This was done using formal mathematical arguments, without specifying the nature of the dynamics of the enzyme-substrate complex. In order to provide a physical basis for this unexpected result, we derive an analytical expression for the enzymatic velocity assuming that the enzyme-substrate complex has multiple states and its conformational dynamics is described by rate equations with arbitrary rate constants. By applying our formalism to a complex with two conformations, we show that the unexpected off rate dependence of the velocity can be readily understood: If one of the conformations is unproductive, the system can escape from this "trap" by dissociating, thereby giving the enzyme another chance to form the productive enzyme-substrate complex. We also demonstrate that the nonmonotonic off rate dependence of the enzymatic velocity is possible not only when all off rate constants are identical, but even when they are different. We show that for typical experimentally determined rate constants, the nonmonotonic off rate dependence can occur for micromolar substrate concentrations. Finally, we discuss the relation of this work to the problem of optimizing the flux through singly occupied membrane channels and transporters.

Effects of molecule anchoring and dispersion on nanoscopic friction under electrochemical control.

The application of electric fields is a promising strategy for in situ control of friction. While there have recently been many experimental studies on friction under the influence of electric fields, theoretical understanding is very limited. Recently, we introduced a simple theoretical model for friction under electrochemical conditions that focused on the interaction of a force microscope tip with adsorbed molecules whose orientation was dependent on the applied electric field. Here we focus on the effects of anchoring of the molecules on friction. We show that anchoring affects the intensity and width of the peak in the friction that occurs near a reorientation transition of adsorbed molecules, and explain this by comparing the strength of molecule-molecule and molecule-tip interactions. We derive a dispersion relation for phonons in the layer of adsorbed molecules and demonstrate that it can be used to understand important features of the frictional response.

Saltatory drift in a randomly driven two-wave potential.

The dynamics of a classical particle in a one-dimensional, randomly driven potential is analysed both analytically and numerically. The potential considered here is composed of two identical spatially periodic saw-tooth-like components, one of which is externally driven by a random force. We show that under certain conditions the particle may travel against the averaged external force, performing a saltatory unidirectional drift with a constant velocity. Such a behaviour persists also in situations when the external force averages out to zero. We demonstrate that the physics behind this phenomenon stems from a particular behaviour of fluctuations in random force: upon reaching a certain level, random fluctuations exercise a locking function creating points of irreversibility which the particle cannot overpass. Repeated (randomly) in each cycle, this results in a saltatory unidirectional drift. This mechanism resembles the work of an escapement-type device in watches. Considering the overdamped limit, we propose simple analytical estimates for the particle's terminal velocity.

Actin-based motility: cooperative symmetry-breaking and phases of motion.

A microscopic model is proposed for the motility of a bead driven by the polymerization of actin filaments. The model exhibits a rich spectrum of behaviours similar to those observed in biomimetic experiments, which include spontaneous symmetry-breaking, various regimes of the bead's motion and correlations between the structure of the actin tail which propels the bead and the bead dynamics. The dependences of the dynamical properties (such as symmetry-breaking time, regimes of motion, mean velocity, and tail asymmetry) on the physical parameters (the bead radius and viscosity) agree well with the experimental observations. We find that most experimental observations can be reproduced taking into account only one type of filaments interacting with the bead: the detached filaments that push the bead. Our calculations suggest that the analysis of mean characteristics only (velocities, symmetry-breaking times, etc) does not always provide meaningful information about the mechanism of motility. The aim should be to obtain the corresponding distributions, which might be extremely broad and therefore not well represented by their mean only. Our findings suggest a simple coarse-grained description, which captures the main features obtained within the microscopic model.

The breakdown of superlubricity by driving-induced commensurate dislocations.

In the framework of a Frenkel-Kontorova-like model, we address the robustness of the superlubricity phenomenon in an edge-driven system at large scales, highlighting the dynamical mechanisms leading to its failure due to the slider elasticity. The results of the numerical simulations perfectly match the length critical size derived from a parameter-free analytical model. By considering different driving and commensurability interface configurations, we explore the distinctive nature of the transition from superlubric to high-friction sliding states which occurs above the critical size, discovering the occurrence of previously undetected multiple dissipative jumps in the friction force as a function of the slider length. These driving-induced commensurate dislocations in the slider are then characterized in relation to their spatial localization and width, depending on the system parameters. Setting the ground to scale superlubricity up, this investigation provides a novel perspective on friction and nanomanipulation experiments and can serve as a theoretical basis for designing high-tech devices with specific superlow frictional features.

Electrotunable lubricity with ionic liquid nanoscale films.

One of the main challenges in tribology is finding the way for an in situ control of friction without changing the lubricant. One of the ways for such control is via the application of electric fields. In this respect a promising new class of lubricants is ionic liquids, which are solvent-free electrolytes, and their properties should be most strongly affected by applied voltage. Based on a minimal physical model, our study elucidates the connection between the voltage effect on the structure of the ionic liquid layers and their lubricating properties. It reveals two mechanisms of variation of the friction force with the surface charge density, consistent with recent AFM measurements, namely via the (i) charge effect on normal and in-plane ordering in the film and (ii) swapping between anion and cation layers at the surfaces. We formulate conditions that would warrant low friction coefficients and prevent wear by resisting "squeezing-out" of the liquid under compression. These results give a background for controllable variation of friction.

Manipulation of dynamical systems by symmetry breaking.

We propose an approach to manipulate and control transport in Hamiltonian systems which are characterized by a mixed phase space. The approach is based on symmetry breaking of the phase space structure by applying a zero-mean periodic force for a finite duration of time. This induces time and space reversal asymmetry, which modifies the internal dynamics of the system and leads to directed transport. It is shown that our strategy allows to perform manipulations both with individual particles and with statistical ensembles of particles.

Ballistic flights and random diffusion as building blocks for Hamiltonian kinetics.

We propose a kinetic approach to transport in Hamiltonian systems with a mixed phase space. The approach is based on the decomposition of the dynamical picture into two contributions: (a) ballistic flights, and (b) random diffusion. The kinetic scheme leads to a stochastic process with statistical properties which are similar to those produced by the original Hamiltonian. We show that our approach helps in obtaining an insight into several properties of Hamiltonian kinetics such as anomalous diffusion, chaos-assisted population exchange, and current rectification. In particular, the chaos-assisted exchange offers a classical counterpart for the recently reported chaos-assisted tunneling.

From deterministic dynamics to kinetic phenomena.

We investigate a one-dimensional Hamiltonian system that describes a system of particles interacting through short-range repulsive potentials. Depending on the particle mean energy epsilon the system demonstrates a spectrum of kinetic regimes, characterized by their transport properties ranging from ballistic motion to localized oscillations through anomalous diffusion regimes. We establish relationships between the observed kinetic regimes and the "thermodynamic" states of the system. The nature of heat conduction in the proposed model is discussed.

Directed molecular transport in an oscillating symmetric channel.

A mechanism responsible for the directed transport and molecular separation in a symmetric channel is proposed. We found that under the action of spatial harmonic oscillations of the channel, the system exhibits a directed transport in either direction, presenting multiple current reversals as the amplitude and/or frequency of the oscillations are varied. The particles of different masses may be forced to move with different velocities in the same or in the opposite directions by properly adjusting driving parameters. The directed transport can be produced in both directions even in the absence of thermal noise; the latter can speed up or slow down the transport depending on the system parameters.