Near-Field, On-Chip Optical Brownian Ratchets

Engineering ratchet-based particle separation via extended shortcuts to isothermality

Microscopic particle separation plays a vital role in various scientific and industrial domains. Conventional separation methods relying on external forces or physical barriers inherently exhibit limitations in terms of efficiency, selectivity, and adaptability across diverse particle types. To overcome these limitations, researchers are constantly exploring new separation approaches, among which ratchet-based separation is a noteworthy method. However, in contrast to the extensive numerical studies and experimental investigations on ratchet separation, its theoretical exploration appears weak, particularly lacking in the analysis of energy consumption involved in the separation processes. The latter is of significant importance for achieving energetically efficient separation. In this paper, we propose a nonequilibrium thermodynamic approach, extending the concept of shortcuts to isothermality, to realize controllable separation of overdamped Brownian particles with low energy cost. By utilizing a designed ratchet potential with temporal period τ, we find in the slow-driving regime that the average particle velocity v[over ¯]_{s}∝(1-D/D^{*})τ^{-1}, indicating that particles with different diffusion coefficients D can be guided to move in distinct directions with a preset D^{*}. It is revealed that an inevitable portion of the energy cost in separation depends on the driving dynamics of the ratchet, with an achievable lower bound W_{ex}^{(min)}∝L^{2}|v[over ¯]_{s}|. Here, L is the thermodynamic length of the driving loop in the parametric space. With a sawtooth potential, we numerically test the theoretical findings and illustrate the optimal separation protocol associated with W_{ex}^{(min)}. Finally, for practical considerations, we compare our approach with the conventional ratchets in terms of separation velocity and energy consumption. The scalability of the current framework for separating various particles in two-dimensional space is also demonstrated. This paper bridges the gap between thermodynamic process control and particle separation, paving the way for further thermodynamic optimization in ratchet-based particle separation.

Molecular Ratchets and Kinetic Asymmetry: Giving Chemistry Direction

Over the last two decades ratchet mechanisms have transformed the understanding and design of stochastic molecular systems-biological, chemical and physical-in a move away from the mechanical macroscopic analogies that dominated thinking regarding molecular dynamics in the 1990s and early 2000s (e.g. pistons, springs, etc), to the more scale-relevant concepts that underpin out-of-equilibrium research in the molecular sciences today. Ratcheting has established molecular nanotechnology as a research frontier for energy transduction and metabolism, and has enabled the reverse engineering of biomolecular machinery, delivering insights into how molecules 'walk' and track-based synthesisers operate, how the acceleration of chemical reactions enables energy to be transduced by catalysts (both motor proteins and synthetic catalysts), and how dynamic systems can be driven away from equilibrium through catalysis. The recognition of molecular ratchet mechanisms in biology, and their invention in synthetic systems, is proving significant in areas as diverse as supramolecular chemistry, systems chemistry, dynamic covalent chemistry, DNA nanotechnology, polymer and materials science, molecular biology, heterogeneous catalysis, endergonic synthesis, the origin of life, and many other branches of chemical science. Put simply, ratchet mechanisms give chemistry direction. Kinetic asymmetry, the key feature of ratcheting, is the dynamic counterpart of structural asymmetry (i.e. chirality). Given the ubiquity of ratchet mechanisms in endergonic chemical processes in biology, and their significance for behaviour and function from systems to synthesis, it is surely just as fundamentally important. This Review charts the recognition, invention and development of molecular ratchets, focussing particularly on the role for which they were originally envisaged in chemistry, as design elements for molecular machinery. Different kinetically asymmetric systems are compared, and the consequences of their dynamic behaviour discussed. These archetypal examples demonstrate how chemical systems can be driven inexorably away from equilibrium, rather than relax towards it.

Electromagnetic Forces and Torques: From Dielectrophoresis to Optical Tweezers

Electromagnetic forces and torques enable many key technologies, including optical tweezers or dielectrophoresis. Interestingly, both techniques rely on the same physical process: the interaction of an oscillating electric field with a particle of matter. This work provides a unified framework to understand this interaction both when considering fields oscillating at low frequencies─dielectrophoresis─and high frequencies─optical tweezers. We draw useful parallels between these two techniques, discuss the different and often unstated assumptions they are based upon, and illustrate key applications in the fields of physical and analytical chemistry, biosensing, and colloidal science.

Brownian ratchet for directional nanoparticle transport by repetitive stretch-relaxation of DNA

Brownian motion subject to a periodic and asymmetric potential can be biased by external, nonequilibrium fluctuations, leading to directional movement of Brownian particles. Sequence-dependent flexibility variation along double-stranded DNA has been proposed as a tool to develop periodic and asymmetric potentials for DNA binding of cationic nanoparticles with sizes below tens of nanometers. Here, we propose that repetitive stretching and relaxation of a long, double-stranded DNA molecule with periodic flexibility gradient can induce nonequilibrium fluctuations that tune the amplitude of asymmetric potentials for DNA-nanoparticle binding to result in directional transport of nanometer-sized particles along DNA. Realization of the proposed Brownian ratchet was proven by Brownian dynamics simulations of coarse-grained models of a single, long DNA molecule with flexibility variation and a cationic nanoparticle.

The role of temperature-induced effects generated by plasmonic nanostructures on particle delivery and manipulation: a review

Plasmonic optical tweezers that stem from the need to trap and manipulate ever smaller particles using non-invasive optical forces, have made significant contributions to precise particle motion control at the nanoscale. In addition to the optical forces, other effects have been explored for particle manipulation. For instance, the plasmonic heat delivery mechanism generates micro- and nanoscale optothermal hydrodynamic effects, such as natural fluid convection, Marangoni fluid convection and thermophoretic effects that influence the motion of a wide range of particles from dielectric to biomolecules. In this review, a discussion of optothermal effects generated by heated plasmonic nanostructures is presented with a specific focus on applications to optical trapping and particle manipulation. It provides a discussion on the existing challenges of optothermal mechanisms generated by plasmonic optical tweezers and comments on their future opportunities in life sciences.

Brownian particles driven by spatially periodic noise

We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can be integrated formally exactly. We determine the short- and long-time behaviour of the mean displacement (MD) and mean-squared displacement (MSD). In particular, we find a very slow dynamics for the mean displacement, scaling as [Formula: see text] with time t. Placed under an additional external periodic force near the critical tilt value we compute the stationary current obtained from the corresponding Fokker-Planck equation and identify an essential singularity if the minimum of the noise strength is zero. Finally, in order to further elucidate the effect of the random periodic driving on the diffusion process, we introduce a phase factor in the spatial noise with respect to the external periodic force and identify the value of the phase shift for which the random force exerts its strongest effect on the long-time drift velocity and diffusion coefficient.

Thermally active nanoparticle clusters enslaved by engineered domain wall traps

The stable assembly of fluctuating nanoparticle clusters on a surface represents a technological challenge of widespread interest for both fundamental and applied research. Here we demonstrate a technique to stably confine in two dimensions clusters of interacting nanoparticles via size-tunable, virtual magnetic traps. We use cylindrical Bloch walls arranged to form a triangular lattice of ferromagnetic domains within an epitaxially grown ferrite garnet film. At each domain, the magnetic stray field generates an effective harmonic potential with a field tunable stiffness. The experiments are combined with theory to show that the magnetic confinement is effectively harmonic and pairwise interactions are of dipolar nature, leading to central, strictly repulsive forces. For clusters of magnetic nanoparticles, the stationary collective states arise from the competition between repulsion, confinement and the tendency to fill the central potential well. Using a numerical simulation model as a quantitative map between the experiments and theory we explore the field-induced crystallization process for larger clusters and unveil the existence of three different dynamical regimes. The present method provides a model platform for investigations of the collective phenomena emerging when strongly confined nanoparticle clusters are forced to move in an idealized, harmonic-like potential.

Antiresonant driven systems for particle manipulation

We report on the onset of antiresonant behavior of mass transport systems driven by time-dependent forces. Antiresonances arise from the coupling of a sufficiently high number of space-time modes of the force. The presence of forces having a wide space-time spectrum, a necessary condition for the formation of an antiresonance, is typical of confined systems with uneven and deformable walls that induce entropic forces dependent on space and time. We have analyzed, in particular, the case of polymer chains confined in a flexible channel and shown how they can be sorted and trapped. The presence of resonance-antiresonance pairs found can be exploited to design protocols able to engineer optimal transport processes and to manipulate the dynamics of nano-objects.

Optical conveyor belt based on a plasmonic metasurface with polarization dependent hot spot arrays

In this Letter, we propose a novel metasurface conveyor belt with periodic orientated arrays of gold plasmonic elliptical elements (GPEEs), which can be continuously lit in a relay way by switching the polarization of the excitation beam and can be used to trap, transport, and sort particles. The array of the hot field can provide a larger trapping area and better stiffness. With the incident optical intensity of 0.08mW/µm², the depth of the potential well could be as high as 10K_BT. By setting a narrow interval between plasmonic ellipses in principal axes, it can help further enhance their directional resonant coupling and polarization dependence. Furthermore, based on consideration of the Brownian motion of trapped particles in aqueous solution, we analyzed its time response property of particle manipulation with different applied switching frequencies from a statistical point of view. As confirmed by numerical analysis, our design offers a novel scheme of particle sorting using a scalable hot spot array with better performance, which could be used in many on-chip optofluidic applications.

Coherently tunable metalens tweezers for optofluidic particle routing

Nanophotonic particle manipulation exploits unique light shaping capabilities of nanophotonic devices to trap, guide, rotate and propel particles in microfluidic channels. Recent introduction of metalens into microfluidics research demonstrates the new capability of using nanophotonics devices for far-field optical manipulation. In this work we demonstrate, via numerical simulation, the first tunable metalens tweezers that function under dual-beam illumination. The phase profile of the metalens is modulated by controlling the relative strength and phase of the two coherent incident light beams. As a result, the metalens creates a thin sheet of focus inside a microchannel. Changes to the illumination condition allow the focus to be swept across the microchannel, thereby producing a controllable and reconfigurable path for particle transport. Particle routing in a Y-branch junction, for both nano- and microparticles, is evaluated as an example functionality for the tunable metalens tweezers. This work shows that tunable far-field particle manipulation can be achieved using near-field nano-engineering and coherent control, opening a new way for the integration of nanophotonics and microfluidics.

Optical Forces: From Fundamental to Biological Applications

Optical forces, generally arising from changes of field gradients or linear momentum carried by photons, form the basis for optical trapping and manipulation. Advances in optical forces help to reveal the nature of light-matter interactions, giving answers to a wide range of questions and solving problems across various disciplines, and are still yielding new insights in many exciting sciences, particularly in the fields of biological technology, material applications, and quantum sciences. This review focuses on recent advances in optical forces, ranging from fundamentals to applications for biological exploration. First, the basics of different types of optical forces with new light-matter interaction mechanisms and near-field techniques for optical force generation beyond the diffraction limit with nanometer accuracy are described. Optical forces for biological applications from in vitro to in vivo are then reviewed. Applications from individual manipulation to multiple assembly into functional biophotonic probes and soft-matter superstructures are discussed. At the end future directions for application of optical forces for biological exploration are provided.

Nanoparticle trapping and routing on plasmonic nanorails in a microfluidic channel

Plasmonic nanostructures hold great promise for enabling advanced optical manipulation of nanoparticles in microfluidic channels, resulting from the generation of strong and controllable light focal points at the nanoscale. A primary remaining challenge in the current integration of plasmonics and microfluidics is to transport trapped nanoparticles along designated routes. Here we demonstrate through numerical simulation a plasmonic nanoparticle router that can trap and route a nanoparticle in a microfluidic channel with a continuous fluidic flow. The nanoparticle router contains a series of gold nanostrips on top of a continuous gold film. The nanostrips support both localised and propagating surface plasmons under light illumination, which underpin the trapping and routing functionalities. The nanoparticle guiding at a Y-branch junction is enabled by a small change of 50 nm in the wavelength of incident light.

Controlling the preferential motion of chiral molecular walkers on a surface

Molecular walkers standing on two or more "feet" on an anisotropic periodic potential of a crystal surface may perform a one-dimensional Brownian motion at the surface-vacuum interface along a particular direction in which their mobility is the largest. In thermal equilibrium the molecules move with equal probabilities both ways along this direction, as expected from the detailed balance principle, well-known in chemical reactivity and in the theory of molecular motors. For molecules that possess an asymmetric potential energy surface (PES), we propose a generic method based on the application of a time-periodic external stimulus that would enable the molecules to move preferentially in a single direction thereby acting as Brownian ratchets. To illustrate this method, we consider a prototypical synthetic chiral molecular walker, 1,3-bis(imidazol-1-ylmethyl)-5(1-phenylethyl)benzene, diffusing on the anisotropic Cu(110) surface along the Cu rows. As unveiled by our kinetic Monte Carlo simulations based on the rates calculated using ab initio density functional theory, this molecule moves to the nearest equivalent lattice site via the so-called inchworm mechanism in which it steps first with the rear foot and then with the front foot. As a result, the molecule diffuses via a two-step mechanism, and due to its inherent asymmetry, the corresponding PES is also spatially asymmetric. Taking advantage of this fact, we show how the external stimulus can be tuned to separate molecules of different chirality, orientation and conformation. The consequences of these findings for molecular machines and the separation of enantiomers are also discussed.

Quo vadis, plasmonic optical tweezers?

Conventional optical tweezers based on traditional optical microscopes are subject to the diffraction limit, making the precise trapping and manipulation of very small particles challenging. Plasmonic optical tweezers can surpass this constraint, but many potential applications would benefit from further enhanced performance and/or expanded functionalities. In this Perspective, we discuss trends in plasmonic tweezers and describe important opportunities presented by its interdisciplinary combination with other techniques in nanoscience. We furthermore highlight several open questions concerning fundamentals that are likely to be important for many potential applications.

In silico construction of a flexibility-based DNA Brownian ratchet for directional nanoparticle delivery

Brownian particles confined in a system with periodic and asymmetric potential can be transported in a specific direction along the potential by repetitively switching the potential on and off. Here, we propose a DNA-based Brownian ratchet for directional transport of positively charged nanoparticles in which nanoparticle delivery follows the path dictated by a single, long, double-stranded DNA. We performed Brownian dynamics simulations to prove its realization using coarse-grained models. A periodic and asymmetric potential for nanoparticle binding is constructed along a single, long, double-stranded DNA molecule by a novel strategy that uses variation in sequence-dependent DNA flexibility. Directional and processive motion of nanoparticles is achieved by changing salt concentration repetitively over several cycles to switch the asymmetric potential on and off. This work suggests that double-stranded DNA molecules with elaborately designed flexibility variation can be used as a molecule-scale guide for spatial and dynamic control of nanoparticles for future applications.

High-temperature ratchets driven by deterministic and stochastic fluctuations

We consider the overdamped dynamics of a Brownian particle in an arbitrary spatial periodic and time-dependent potential on the basis of an exact solution for the probability density in the form of a power series in the inverse friction coefficient. The expression for the average velocity of a Brownian ratchet is simplified in the high-temperature consideration when only the first terms of the series can be used. For the potential of an additive-multiplicative form (a sum of a time-independent contribution and a time-dependent multiplicative perturbation), general explicit expressions are obtained which allow comparative analysis of frequency dependencies of the average velocity, implying deterministic and stochastic potential energy fluctuations. For qualitative and quantitative analysis of these dependences, we choose illustrative examples for spatial harmonic fluctuations: with deterministic time dependences of a relaxation type and stochastic time dependences describing Markovian dichotomous and harmonic noise processes. We explore the influence of fluctuation types on the ratchet effect and demonstrate its enhancement in the case of harmonic noise.

Enhancing Nanoparticle Diffusion on a Unidirectional Domain Wall Magnetic Ratchet

The performance of nanoscale magnetic devices is often limited by the presence of thermal fluctuations, whereas in micro- and nanofluidic applications the same fluctuations may be used to spread reactants or drugs. Here, we demonstrate the controlled motion and the enhancement of diffusion of magnetic nanoparticles that are manipulated and driven across a series of Bloch walls within an epitaxially grown ferrite garnet film. We use a rotating magnetic field to generate a traveling wave potential that unidirectionally transports the nanoparticles at a frequency tunable speed. Strikingly, we find an enhancement of diffusion along the propulsion direction and a frequency-dependent diffusion coefficient that can be precisely controlled by varying the system parameters. To explain the reported phenomena, we develop a theoretical approach that shows a fair agreement with the experimental data enabling an exact analytical expression for the enhanced diffusivity above the magnetically modulated periodic landscape. Our technique to control thermal fluctuations of driven magnetic nanoparticles represents a versatile and powerful way to programmably transport magnetic colloidal matter in a fluid, opening the doors to different fluidic applications based on exploiting magnetic domain wall ratchets.

Tunable size selectivity and nanoparticle immobilization on a photonic crystal optical trap

We harness residual thermal effects in a low-absorptivity system to manipulate parallel optical trapping of particles on the nanoscale. A photonic crystal is used to generate a 2D array of optical traps. We show that the size selectivity of the trap can be tuned by adding a non-ionic surfactant to the solution, altering the thermophoretic effect that delivers nanoparticles to trapping sites. We further show that particles can be permanently immobilized on the photonic crystal via photopolymerization of the trapping medium.

Inhomogeneity-Induced Casimir Transport of Nanoparticles

We propose a scheme for transporting nanoparticles immersed in a fluid, relying on quantum vacuum fluctuations. The mechanism lies in the inhomogeneity-induced lateral Casimir force between a nanoparticle and a gradient metasurface and the relaxation of the conventional Dzyaloshinskiǐ-Lifshitz-Pitaevskiǐ constraint, which allows quantum levitation for a broader class of material configurations. The velocity for a nanosphere levitated above a grating is calculated and can be up to a few microns per minute. The Born approximation gives general expressions for the Casimir energy which reveal size-selective transport. For any given metasurface, a certain particle-metasurface separation exists where the transport velocity peaks, forming a "Casimir passage." The sign and strength of the Casimir interactions can be tuned by the shapes of liquid-air menisci, potentially allowing real-time control of an otherwise passive force, and enabling interesting on-off or directional switching of the transport process.

Dimensional reduction of a general advection-diffusion equation in 2D channels

Diffusion of point-like particles in a two-dimensional channel of varying width is studied. The particles are driven by an arbitrary space dependent force. We construct a general recurrence procedure mapping the corresponding two-dimensional advection-diffusion equation onto the longitudinal coordinate x. Unlike the previous specific cases, the presented procedure enables us to find the one-dimensional description of the confined diffusion even for non-conservative (vortex) forces, e.g. caused by flowing solvent dragging the particles. We show that the result is again the generalized Fick-Jacobs equation. Despite of non existing scalar potential in the case of vortex forces, the effective one-dimensional scalar potential, as well as the corresponding quasi-equilibrium and the effective diffusion coefficient [Formula: see text] can be always found.

Optical tweezing using tunable optical lattices along a few-mode silicon waveguide

Fourteen years ago, optical lattices and holographic tweezers were considered as a revolution, allowing for trapping and manipulating multiple particles at the same time using laser light. Since then, near-field optical forces have aroused tremendous interest as they enable efficient trapping of a wide range of objects, from living cells to atoms, in integrated devices. Yet, handling at will multiple objects using a guided light beam remains a challenging task for current on-chip optical trapping techniques. We demonstrate here on-chip optical trapping of dielectric microbeads and bacteria using one-dimensional optical lattices created by near-field mode beating along a few-mode silicon nanophotonic waveguide. This approach allows not only for trapping large numbers of particles in periodic trap arrays with various geometries, but also for manipulating them via diverse transport and repositioning techniques. Near-field mode-beating optical lattices may be readily implemented in lab-on-a-chip devices, addressing numerous scientific fields ranging from bio-analysis to nanoparticle processing.

Two-dimensional arbitrary nano-manipulation on a plasmonic metasurface

In this Letter, we report on a plasmonic nano-ellipse metasurface with the purpose of trapping and two-dimensional (2D) arbitrary transport of nanoparticles by means of rotating the polarization of an excitation beam. The locations of hot spots within a metasurface are polarization dependent, thus making it possible to turn on/off the adjacent hot spots and then convey the trapped target by rotating the incident polarization state. For the case of a metasurface with a unit cell of perpendicularly orientated nano-ellipses, the hot spots with higher intensities are located at both apexes of the nano-ellipse whose major axis is parallel to the direction of polarization. When the polarization gradually rotates to its counterpart direction, the trapped particle may move around the ellipse and transfer to the most adjacent ellipse, due to the unbalanced trap potentials around the nano-ellipse. Clockwise and counterclockwise rotation would guide the particle in a different direction, which makes it possible to convey the particle arbitrarily within the plasmonic metasurface by setting a time sequence of polarization rotation. As confirmed by the three-dimensional finite-difference time-domain analysis, our design offers a novel scheme of 2D arbitrary transport with nanometer accuracy, which could be used in many on-chip optofluidic applications.

How To Drive a Flashing Electron Ratchet To Maximize Current

Biological systems utilize a combination of asymmetry, noise, and chemical energy to produce motion in the highly damped environment of the cell with molecular motors, many of which are "ratchets", nonequilibrium devices for producing directed transport using nondirectional perturbations without a net bias. The underlying ratchet principle has been implemented in man-made micro- and nanodevices to transport charged particles by oscillating an electric potential with repeating asymmetric features. In this experimental study, the ratcheting of electrons in an organic semiconductor is optimized by tuning the temporal modulation of the oscillating potential, applied using nanostructured electrodes. An analytical model of steady-state carrier dynamics is used to determine that symmetry-breaking motion of carriers through the thickness of the polymer layer enables even temporally unbiased waveforms (e.g., sine) to produce current, an advance that could allow the future use of electromagnetic radiation to power ratchets. The analysis maps the optimal operating frequency of the ratchet to the mobility of the transport layer and the spatial periodicity of the potential, and relates the dependence on the temporal waveform to the dielectric characteristics and thickness of the layer.

Omnidirectional Transport in Fully Reconfigurable Two Dimensional Optical Ratchets

A fully reconfigurable two-dimensional (2D) rocking ratchet system created with holographic optical micromanipulation is presented. We can generate optical potentials with the geometry of any Bravais lattice in 2D and introduce a spatial asymmetry with arbitrary orientation. Nontrivial directed transport of Brownian particles along different directions is demonstrated numerically and experimentally, including on axis, perpendicular, and oblique with respect to an unbiased ac driving. The most important aspect to define the current direction is shown to be the asymmetry and not the driving orientation, and yet we show a system in which the asymmetry orientation of each potential well does not coincide with the transport direction, suggesting an additional symmetry breaking as a result of a coupling with the lattice configuration. Our experimental device, due to its versatility, opens up a new range of possibilities in the study of nonequilibrium dynamics at the microscopic level.