Experimental Observation of Current Reversal in a Rocking Brownian Motor

Memory-induced current reversal of Brownian motors

The kinetics of biological motors such as kinesin or dynein is notably influenced by a viscoelastic intracellular environment. The characteristic relaxation time of the cytosol is not separable from the colloidal timescale and therefore their dynamics is inherently non-Markovian. In this paper, we consider a variant of a Brownian motor model, namely, a Brownian ratchet immersed in a correlated thermal bath, and we analyze how memory influences its dynamics. In particular, we demonstrate the memory-induced current reversal effect and explain this phenomenon by applying the effective mass approximation as well as uncovering the memory-induced dynamical localization of the motor trajectories in the phase space. Our results reveal new aspects of the role of memory in microscopic systems out of thermal equilibrium.

Ratchet effect and jamming in dense mixtures of active and passive colloids in narrow pores

Using the framework of generalized exclusion processes, we study mixtures of passive and active particles interacting by steric repulsion. The particles move in a pore with a periodically modulated aperture, which is modeled by a quasi-one-dimensional channel with a periodic tooth-shaped profile. Internal driving of the active particles induces a ratchet current of these particles. In the current-density diagram, we observe three main regimes: of free flow, of thermally activated processes, and of spinodal decomposition. When the density of particles is increased, we observe a transition to a jammed state, where the ratchet current is substantially reduced. In time evolution, the transition to a jammed state is seen as a sudden drop of current at a certain time. The probability distribution of these jamming times follows an exponential law. The average jamming time depends exponentially on the density of active particles. The coefficient in this exponential is nearly independent of the switching rate of the active particles as well as the presence or absence of passive particles. Due to the interaction, the current of active particles imposes a drag on the passive particles. In the limit of both large systems and long times, the current of passive particles always has the same direction as the ratchet current of active particles. However, during the evolution of the system, we observe a very slow (logarithmic in time) approach to the asymptotic value, sometimes accompanied by current reversal, i.e., the current of active and passive particles may go in opposite directions.

Brownian motors powered by nonreciprocal interactions

Traditional models for molecular (Brownian) motors predominantly depend on nonequilibrium driving, while particle interactions rigorously adhere to Newton's third law. However, numerous living and natural systems at various scales seem to defy this well-established law. In this study, we investigated the transport of mixed Brownian particles in a two-dimensional ratchet potential with nonreciprocal interactions. Our findings reveal that these nonreciprocal interactions can introduce a zero-mean nonequilibrium driving force. This force is capable of disrupting the thermodynamic equilibrium and inducing directed motion. The direction of this motion is determined by the asymmetry of the potential. Interestingly, the average velocity is a peaked function of the degree of nonreciprocity, while the effective diffusion consistently increases with the increase of nonreciprocity. There exists an optimal temperature or packing fraction at which the average velocity reaches its maximum value. We share a mechanism for particle rectification, devoid of particle-autonomous nonequilibrium drive, with potential usage in systems characterized by nonreciprocal interactions.

Mechanochemical active ratchet

Self-propelled nanoparticles moving through liquids offer the possibility of creating advanced applications where such nanoswimmers can operate as artificial molecular-sized motors. Achieving control over the motion of nanoswimmers is a crucial aspect for their reliable functioning. While the directionality of micron-sized swimmers can be controlled with great precision, steering nano-sized active particles poses a real challenge. One of the reasons is the existence of large fluctuations of active velocity at the nanoscale. Here, we describe a mechanism that, in the presence of a ratchet potential, transforms these fluctuations into a net current of active nanoparticles. We demonstrate the effect using a generic model of self-propulsion powered by chemical reactions. The net motion along the easy direction of the ratchet potential arises from the coupling of chemical and mechanical processes and is triggered by a constant, transverse to the ratchet, force. The current magnitude sensitively depends on the amplitude and the periodicity of the ratchet potential and the strength of the transverse force. Our results highlight the importance of thermodynamically consistent modeling of chemical reactions in active matter at the nanoscale and suggest new ways of controlling dynamics in such systems.

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

Collective particle transport across periodic energy landscapes is ubiquitously present in many condensed matter systems spanning from vortices in high-temperature superconductors, frictional atomic sliding, driven skyrmions to biological and active matter. Here we report the emergence of fast solitons propagating against a rotating optical landscape. These experimentally observed solitons are stable cluster waves that originate from a coordinated particle exchange process which occurs when the number of trapped microparticles exceeds the number of potential wells. The size and speed of individual solitons rapidly increase with the particle diameter as predicted by theory and confirmed by numerical simulations. We show that when several solitons coexist, an effective repulsive interaction can stabilize their propagation along the periodic potential. Our experiments demonstrate a generic mechanism for cluster-mediated transport with potential applications to condensed matter systems on different length scales.

Roughness induced current reversal in fractional hydrodynamic memory

The existence of a corrugated surface is of great importance and ubiquity in biological systems, exhibiting diverse dynamic behaviors. However, it has remained unclear whether such rough surface leads to the current reversal in fractional hydrodynamic memory. We investigate the transport of a particle within a rough potential under external forces in a subdiffusive media with fractional hydrodynamic memory. The results demonstrate that roughness induces current reversal and a transition from no transport to transport. These phenomena are analyzed through the subdiffusion, Peclet number, useful work, input power, and thermodynamic efficiency. The analysis reveals that transport results from energy conversion, wherein time-dependent periodic force is partially converted into mechanical energy to drive transport against load, and partially dissipated through environmental absorption. In addition, the findings indicate that the size and shape of ratchet tune the occurrence and disappearance of the current reversal, and control the number of times of the current reversal occurring. Furthermore, we find that temperature, friction, and load tune transport, resonant-like activity, and enhanced stability of the system, as evidenced by thermodynamic efficiency. These findings may have implications for understanding dynamics in biological systems and may be relevant for applications involving molecular devices for particle separation at the mesoscopic scale.

Colloidal Stochastic Resonance in Confined Geometries

We investigate the dynamical properties of a colloidal particle in a double cavity. Without external driving, the particle hops between two free-energy minima with transition mean time depending on the system's entropic and energetic barriers. We then drive the particle with a periodic force. When the forcing period is set at twice the transition mean time, a statistical synchronization between particle motion and forcing phase marks the onset of a stochastic resonance mechanism. Comparisons between experimental results and predictions from the Fick-Jacobs theory and Brownian dynamics simulation reveal significant hydrodynamic effects, which change both resonant amplification and noise level. We further show that hydrodynamic effects can be incorporated into existing theory and simulation by using an experimentally measured particle diffusivity.

Collective transient ratchet transport induced by many elastically interacting particles

Several dynamical systems in nature can be maintained out-of-equilibrium, either through mutual interaction of particles or by external fields. The particle’s transport and the transient dynamics are landmarking of such systems. While single ratchet systems are genuine candidates to describe unbiased transport, we demonstrate here that coupled ratchets exhibit collective transient ratchet transport. Extensive numerical simulations for up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N=1024$$\end{document}N=1024 elastically interacting ratchets establish the generation of large transient ratchet currents (RCs). The lifetimes of the transient RCs increase with N and decrease with the coupling strength between the ratchets. We demonstrate one peculiar case having a coupling-induced transient RC through the asymmetric destruction of attractors. Results suggest that physical devices built with coupled ratchet systems should present large collective transient transport of particles, whose technological applications are undoubtedly appealing and feasible.

Phonon-Induced Ratchet Motion of a Water Nanodroplet on a Supported Black Phosphorene

Phonons are not supposed to carry any physical momentum as lattice vibrational modes; thus, it is believed no mass transport could be induced by phonons. In this Letter, we show that a ratchet motion of a water nanodroplet could be induced on a two-dimensional puckered lattice like black phosphorene (BP) by exciting its flexural phonons through a moving substrate. The water nanodroplet exhibits a forward motion along the armchair or a backward motion along the zigzag directions on a BP lattice that is supported on a substrate possessing a relative armchair or zigzag forward motion with BP. Through the analysis of the structure and vibrational density states of BP, it is found that in-plane lattice displacement asymmetry and the in-plane vibration asymmetry are induced by the excited flexural phonons, which determine the water nanodroplet motion as an anisotropic Brownian motor. Simulations of the nanodroplet motion as functions of the substrate relative motion speed and direction and also the substrate coupling strength with BP are performed. Results of the nanodroplet ratchet motion exhibit good agreement with the theoretical predications from calculating the Brownian motor asymmetry. Our findings reveal a promising mass transport strategy and a further understanding of phonon-related interactions in crystalline solids.

Nanoscale directional motion by angustotaxis

Directing motion of a nanoscale object on solid surfaces, in particular in an intrinsic way, is crucial for many aspects of nanotechnology applications. Here we report a novel intrinsic mechanism for nanoscale directional motion, termed angustotaxis, where a wide single walled carbon nanotube in a tapered channel drives itself toward the narrower end of the channel. The underlying physics of angustotaxis is attributed to the lower system potential when the nanotube is at a narrower region of the channel due to the increased contact area between the nanotube and the channel. Angustotaxis could lead to promising routes not only for nanoscale energy conversion from van der Waals potential to mechanical work, but also for mass transport like surface cleaning.

Separation of dense colloidal suspensions in narrow channels: A stochastic model

The flow of a colloidal suspension in a narrow channel of periodically varying width is described by the one-dimensional generalized asymmetric exclusion process. Each site admits multiple particle occupancy. We consider particles of two different sizes. The sites available to particles form a comblike geometry: entropic traps due to variation of channel width are modeled by dead ends, or pockets, attached individually to each site of a one-dimensional chain. This geometry, combined with periodically alternating external driving, leads to a ratchet effect which is very sensitive to particle size, thus enabling particle sorting. A typical behavior is reversal of the current orientation when we change the density of small and big particles. In an optimal situation, the two types of particles move in opposite directions, and particle separation is in principle perfect. We show that in the simplest situation with one type of particles only, this model is exactly soluble. In the general case we use enhanced mean-field approximation as well as direct numerical simulations.

Thermal scanning probe lithography-a review

Fundamental aspects and state-of-the-art results of thermal scanning probe lithography (t-SPL) are reviewed here. t-SPL is an emerging direct-write nanolithography method with many unique properties which enable original or improved nano-patterning in application fields ranging from quantum technologies to material science. In particular, ultrafast and highly localized thermal processing of surfaces can be achieved through the sharp heated tip in t-SPL to generate high-resolution patterns. We investigate t-SPL as a means of generating three types of material interaction: removal, conversion, and addition. Each of these categories is illustrated with process parameters and application examples, as well as their respective opportunities and challenges. Our intention is to provide a knowledge base of t-SPL capabilities and current limitations and to guide nanoengineers to the best-fitting approach of t-SPL for their challenges in nanofabrication or material science. Many potential applications of nanoscale modifications with thermal probes still wait to be explored, in particular when one can utilize the inherently ultrahigh heating and cooling rates.

Deterministic Deposition of Nanoparticles with Sub-10 nm Resolution

Accurate deposition of nanoparticles at defined positions on a substrate is still a challenging task, because it requires simultaneously stable long-range transport and attraction to the target site and precise short-range orientation and deposition. Here we present a method based on geometry-induced energy landscapes in a nanofluidic slit for particle manipulation: Brownian motors or electro-osmotic flows are used for particle delivery to the target area. At the target site, electrostatic trapping localizes and orients the particles. Finally, reducing the gap distance of the slit leads sequentially to a focusing of the particle position and a jump into adhesive contact by several nanometers. For 60 nm gold spheres, we obtain a placement accuracy of 8 nm. The versatility of the method is demonstrated further by a stacked assembly of nanorods and the directed deposition of InAs nanowires.

Single-file transport in periodic potentials: The Brownian asymmetric simple exclusion process

Single-file Brownian motion in periodic structures is an important process in nature and technology, which becomes increasingly amenable for experimental investigation under controlled conditions. To explore and understand generic features of this motion, the Brownian asymmetric simple exclusion process (BASEP) was recently introduced. The BASEP refers to diffusion models where hard spheres are driven by a constant drag force through a periodic potential. Here we derive general properties of the rich collective dynamics in the BASEP. Average currents in the steady state change dramatically with the particle size and density. For an open system coupled to particle reservoirs, extremal current principles predict various nonequilibrium phases, which we verify by Brownian dynamics simulations. For general pair interactions we discuss connections to single-file transport by traveling-wave potentials and prove the impossibility of current reversals in systems driven by a constant drag and by traveling waves.

Tunable Mass Separation via Negative Mobility

A prerequisite for isolating diseased cells requires a mechanism for effective mass-based separation. This objective, however, is generally rather challenging because typically no valid correlation exists between the size of the particles and their mass value. We consider an inertial Brownian particle moving in a symmetric periodic potential and subjected to an externally applied unbiased harmonic driving in combination with a constant applied bias. In doing so, we identify a most efficient separation scheme which is based on the anomalous transport feature of negative mobility, meaning that the immersed particles move in the direction opposite to the acting bias. This work is the first of its kind in demonstrating a tunable separation mechanism in which the particle mass targeted for isolation is effectively controlled over a regime of nearly 2 orders of mass magnitude upon changing solely the frequency of the external harmonic driving. This approach may provide mass selectivity required in present and future separation of a diversity of nano- and microsized particles of either biological or synthetic origin.

Geometry-induced local thermal current from cold to hot in a classical harmonic system

The second law of thermodynamics requires the overall thermal current to flow from hot to cold. However, it does not forbid a local thermal current from flowing from cold to hot. By coupling a harmonic system of three masses connected by a few springs to two Langevin reservoirs at different temperatures, a local atypical thermal current is found to flow from cold to hot in the steady state while the overall thermal current is still from hot to cold. The direction of the local thermal current can be tuned by the mass, spring constant, and system-reservoir coupling. The local thermal current can vanish if the parameters are tuned to proper values. We also consider nonlinear effect from the system-substrate coupling and find that the local atypical thermal current survives in the presence of the nonlinear potential. Moreover, the local atypical thermal current is robust against asymmetry of the system-reservoir coupling, inhomogeneity of the nonlinear potential, and additions of more masses and springs. In molecular or nanomechanical systems where the setup may find its realization, the direction of the local thermal current may be controlled by mechanical or electromagnetic means, which may lead to applications in information storage.

Brownian Asymmetric Simple Exclusion Process

We study the driven Brownian motion of hard rods in a one-dimensional cosine potential with a large amplitude compared to the thermal energy. In a closed system, we find surprising features of the steady-state current in dependence of the particle density. The form of the current-density relation changes greatly with the particle size and can exhibit both a local maximum and minimum. The changes are caused by an interplay of a barrier reduction, blocking, and exchange symmetry effect. The latter leads to a current equal to that of noninteracting particles for a particle size commensurate with the period length of the cosine potential. For an open system coupled to particle reservoirs, we predict five different phases of nonequilibrium steady states to occur. Our results show that the particle size can be of crucial importance for nonequilibrium phase transitions in driven systems. Possible experiments for demonstrating our findings are pointed out.