Atomic Scale Friction and Different Phases of Motion of Embedded Molecular Systems

Manipulating Molecular Self-Assembly Process at the Solid-Liquid Interface Probed by Scanning Tunneling Microscopy

The phenomenon of ordered self-assembly on solid substrates is a topic of interest in both fundamental surface science research and its applications in nanotechnology. The regulation and control of two-dimensional (2D) self-assembled supra-molecular structures on surfaces have been realized through applying external stimuli. By utilizing scanning tunneling microscopy (STM), researchers can investigate the detailed phase transition process of self-assembled monolayers (SAMs), providing insight into the interplay between intermolecular weak interactions and substrate-molecule interactions, which govern the formation of molecular self-assembly. This review will discuss the structural transition of self-assembly probed by STM in response to external stimuli and provide state-of-the-art methods such as tip-induced confinement for the alignment of SAM domains and selective chirality. Finally, we discuss the challenges and opportunities in the field of self-assembly and STM.

Occupancy correlations in the asymmetric simple inclusion process

The asymmetric simple inclusion process (ASIP)-a lattice-gas model for unidirectional transport with irreversible aggregation-has been proposed as an inclusion counterpart of the asymmetric simple exclusion process and as a batch service counterpart of the tandem Jackson network. To date, the analytical tractability of the model has been limited: while the average particle density in the model is easy to compute, very little is known about the joint occupancy distribution. To partially bridge this gap, we study occupancy correlations in the ASIP. We take an analytical approach to this problem and derive an exact formula for the covariance matrix of the steady-state occupancy vector. We verify the validity of this formula numerically in small ASIP systems, where Monte Carlo simulations can provide reliable estimates for correlations in reasonable time, and further use it to draw a comprehensive picture of spatial occupancy correlations in ASIP systems of arbitrary size.

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.

Rupture dynamics in model polymer systems

In this paper we explore the rupture dynamics of a model polymer system to capture the microscopic mechanism during relative motion of surfaces at the single polymer level. Our model is similar to the model for friction introduced by Filippov, Klafter, and Urbakh [Filippov et al., Phys. Rev. Lett., 2004, 92, 135503]; but with an important generalization to a flexible transducer (modelled as a bead spring polymer) which is attached to a fixed rigid planar substrate by interconnecting bonds (modelled as harmonic springs), and pulled by a constant force FT. Bonds are allowed to rupture stochastically. The model is simulated, and the results for a certain set of parameters exhibit a sequential rupture mechanism resulting in rupture fronts. A mean field formalism is developed to study these rupture fronts and the possible propagating solutions for the coupled bead and bond dynamics, where the coupling excludes an exact analytical treatment. Numerical solutions to mean field equations are obtained by standard numerical techniques, and they agree well with the simulation results which show sequential rupture. Within a travelling wave formalism based on the Tanh method, we show that the velocity of the rupture front can be obtained in closed form. The derived expression for the rupture front velocity gives good agreement with the stochastic and mean field results, when the rupture is sequential, while propagating solutions for bead and bond dynamics are shown to agree under certain conditions.

Poissonian steady states: from stationary densities to stationary intensities

Markov dynamics are the most elemental and omnipresent form of stochastic dynamics in the sciences, with applications ranging from physics to chemistry, from biology to evolution, and from economics to finance. Markov dynamics can be either stationary or nonstationary. Stationary Markov dynamics represent statistical steady states and are quantified by stationary densities. In this paper, we generalize the notion of steady state to the case of general Markov dynamics. Considering an ensemble of independent motions governed by common Markov dynamics, we establish that the entire ensemble attains Poissonian steady states which are quantified by stationary Poissonian intensities and which hold valid also in the case of nonstationary Markov dynamics. The methodology is applied to a host of Markov dynamics, including Brownian motion, birth-death processes, random walks, geometric random walks, renewal processes, growth-collapse dynamics, decay-surge dynamics, Ito diffusions, and Langevin dynamics.

Asymmetric inclusion process

We introduce and explore the asymmetric inclusion process (ASIP), an exactly solvable bosonic counterpart of the fermionic asymmetric exclusion process (ASEP). In both processes, random events cause particles to propagate unidirectionally along a one-dimensional lattice of n sites. In the ASEP, particles are subject to exclusion interactions, whereas in the ASIP, particles are subject to inclusion interactions that coalesce them into inseparable clusters. We study the dynamics of the ASIP, derive evolution equations for the mean and probability generating function (PGF) of the sites' occupancy vector, obtain explicit results for the above mean at steady state, and describe an iterative scheme for the computation of the PGF at steady state. We further obtain explicit results for the load distribution in steady state, with the load being the total number of particles present in all lattice sites. Finally, we address the problem of load optimization, and solve it under various criteria. The ASIP model establishes bridges between statistical physics and queueing theory as it represents a tandem array of queueing systems with (unlimited) batch service, and a tandem array of growth-collapse processes.

Transition from smooth sliding to stick-slip motion in a single frictional contact

We show that the transition from smooth sliding to stick-slip motion in a single planar frictional junction always takes place at an atomic-scale relative velocity of the substrates.

The nonlinear nature of friction

Tribology is the study of adhesion, friction, lubrication and wear of surfaces in relative motion. It remains as important today as it was in ancient times, arising in the fields of physics, chemistry, geology, biology and engineering. The more we learn about tribology the more complex it appears. Nevertheless, recent experiments coupled to theoretical modelling have made great advances in unifying apparently diverse phenomena and revealed many subtle and often non-intuitive aspects of matter in motion, which stem from the nonlinear nature of the problem.

Boundary lubrication with a glassy interface

Recently introduced constitutive equations for the rheology of dense, disordered materials are investigated in the context of stick-slip experiments in boundary lubrication. The model is based on a generalization of the shear transformation zone (STZ) theory, in which plastic deformation is represented by a population of mesoscopic regions which may undergo nonaffine deformations in response to stress. The generalization we study phenomenologically incorporates the effects of aging and glassy relaxation. Under experimental conditions associated with typical transitions from stick-slip to steady sliding and stop-start tests, these effects can be dominant, although the full STZ description is necessary to account for more complex, chaotic transitions.

Friction through dynamical formation and rupture of molecular bonds

We introduce a model for friction in a system of two rigid plates connected by bonds (springs) and experiencing an external drive. The macroscopic frictional properties of the system are shown to be directly related to the rupture and formation dynamics of the microscopic bonds. Different regimes of motion are characterized by different rates of rupture and formation relative to the driving velocity. In particular, the stick-slip regime is shown to correspond to a cooperative rupture of the bonds. Moreover, the notion of static friction is shown to be dependent on the experimental conditions and time scales. The overall behavior can be described in terms of two Deborah numbers.

Nature of mechanical instabilities and their effect on kinetic friction

It has long been recognized that kinetic friction F(k) between two solids must be due to instabilities, sudden "pops" of certain degrees of freedom. Here, such pops are studied with a focus on boundary lubrication. The pops' characteristics and consequently the friction-velocity relationship depend qualitatively on dimensionality, commensurability, and details of the lubricant wall interaction. It is found that F(k) should be small between commensurate surfaces. F(k) is large for incommensurate surfaces, unless the lubricant's motion is confined to 1D. The effects of thermal noise are discussed and computer simulations are employed to show the relevance of the predictions to less idealized models.

Confined molecules under shear: from a microscopic description to phenomenology

A coarse grained two-state model is derived starting from a molecular dynamics description of a molecular system under shear. This model captures the main features of the response of a confined system under shear, and generalizes the phenomenological Tomlinson model for the response of a driven system. The derivation is based on the solution of coupled microscopic equations using a mean field approximation. The two-state model agrees well with the direct numerical solution and offers a practical approach to investigate the response of sheared systems under a broad range of parameters.

Dynamic phase transitions in confined lubricant fluids under shear

A surface force apparatus was used to measure the transient and steady-state friction forces between molecularly smooth mica surfaces confining thin films of squalane, C30H62, a saturated, branched hydrocarbon liquid. The dynamic friction "phase diagram" was determined under different shearing conditions, especially the transitions between stick-slip and smooth sliding "states" that exhibited a chaotic stick-slip regime. The apparently very different friction traces exhibited by simple spherical, linear, and branched hydrocarbon films under shear are shown to be due to the much longer relaxation times and characteristic length scales associated with transitions from rest to steady-state sliding, and vice versa, in the case of branched liquids. The physical reasons and tribological implications for the different types of transitions observed with spherical, linear, and branched fluids are discussed.