Lane formation of colloidal particles driven in parallel by gravity.

We investigate the lane formation in nonequilibrium systems of colloidal particles moving in parallel that are driven by the force of gravity. For this setup, an experimental implementation of a channel on a slope can be conceptualized. We employ the Brownian dynamics algorithm and confine the repulsive particles with hard walls based on the solution of the Smoluchowski equation in the half space. A difference of the driving force acting on the colloids could be achieved by using two spherical particle types with differing diameters but equal mass density. First, we investigate how a difference in the channel slope affects the lane formation of the systems, after which we analyze the lanes that formed. We find that the large particles push the small particles to the walls, resulting in exclusively small particle lanes at the walls. This contrasts the equilibrium state, where depletion forces push the larger particles to the walls. Additionally, we have a closer look at the mechanisms by which the lanes form. Finally, we find system parameter values that foster lane formation to lay the foundation for an experimental realization of our proposed setup. To round this off, we give an exemplary calculation of the slope angle needed to get the experimental system into a state of lane order. With the examination of lane order in systems that are driven in parallel, we hope to deepen our understanding of nonequilibrium order phenomena.

Capture and transport of rod-shaped cargo via programmable active particles.

We study the influence of the cargo shape on the capture and transport process of colloidal rods via swarms of active particles using Brownian dynamics simulations. Starting at random initial conditions, active particles that interact via the Lennard-Jones potential and possess a tuneable speed are utilised to capture passive rods inside a hexagonal cage of individually addressable units. By adjusting the velocity of the individual active particles, the rod can then be transported. To guarantee a successful capture process (with a strong localisation), we find that specific geometric and energetic constraints have to be met; i.e., the length of the rod must approximately be in the vicinity of an odd multiple of the lattice constant of the hexagonal cage, and the Lennard-Jones interaction strength must be in the range of [Formula: see text] to [Formula: see text]. If the cargo aspect ratio gets too large, the subsequent transport of successfully captured rods can fail. For systems where transport is possible, an increase in the cargo aspect ratio decreases the achievable transport velocity. Our work shows that the particle shape must be considered while designing interaction rules to accomplish specific tasks via groups of controllable units.

Diffusion coefficients of linear trimer particles.

We study the diffusive behavior of linear trimer particles via numerical calculations. First, we utilize hydrodynamic bead-shell calculations to compute the microscopic diffusion coefficients for different particle aspect ratios. These values are then used to obtain continuous empirical formulas for said coefficients. As an application example for the empirical formulas, we perform Brownian dynamics simulations of monolayers consisting of a linear trimer surrounded by colloidal spheres. Here, we obtain empirical formulas for the corresponding long-time diffusion coefficients of the trimer. By comparing our data for the microscopic and long-time diffusion coefficients with known results for spherocylinders, we find that the diffusive behavior of both particle geometries is approximately identical. Based on this observation, we introduce simplified equations for the microscopic diffusion coefficients that can be used for arbitrary short rods that are spheres at the minimum aspect ratios. The calculated equations for the diffusion coefficients can be applied to various further numerical and experimental studies utilizing linear trimer particles.

Lane and band formation of oppositely driven colloidal particles in two-dimensional ring geometries.

We study the segregation phenomena for oppositely driven colloidal particles in two-dimensional ring geometries by means of Brownian dynamics simulations without hydrodynamic interactions. The particles interact via a repulsive Yukawa potential and are confined to a two-dimensional circular channel by hard walls, in which half of the particles are driven clockwise and the other half are driven counterclockwise. In addition to lane formation, which is commonly found in oppositely driven systems, we found band formation along the angular direction in channels with a very large radius. This indicates that a formation of lanes is prevented in the limit of channels with an infinitely large inner radius. The dependency of this segregation has been examined for the two control parameters, the interaction strength between the particles and the width of the circular channel.

Group formation and collective motion of colloidal rods with an activity triggered by visual perception.

We investigate the formation of cohesive groups and the collective diffusion of colloidal spherocylinders with a motility driven by a simple visual perception model. For this, we perform Brownian dynamics simulations without hydrodynamic interactions. The visual perception is based on sight cones attached to the spherocylinders and perception functions quantifying the visual stimuli. If the perception function of a particle reaches a predefined threshold, an active component is added to its motion. We find that, in addition to the opening angle of the cone of sight, the aspect ratio of the particles plays an important role for the formation of cohesive groups. If the elongation of the particles is increased, the maximum angle for which the rods organize themselves into such groups decreases distinctly. After a system forms a cohesive group, it performs a diffusive motion, which can be quantified by an effective diffusion coefficient. For increasing aspect ratios, the spatial expansion of the cohesive groups and the effective diffusion coefficient of the collective motion increase, while the number of active group members decreases. We also find that a larger particle number, a smaller propulsion velocity of the group members, and a smaller threshold for the visual stimulus increase the maximum opening angle for which cohesive groups form. Based on our results, we expect anisotropic particles to be of great relevance for the adjustability of visual perception-dependent motility.

Role of cohesion in the flow of active particles through bottlenecks.

We experimentally and numerically study the flow of programmable active particles (APs) with tunable cohesion strength through geometric constrictions. Similar to purely repulsive granular systems, we observe an exponential distribution of burst sizes and power-law-distributed clogging durations. Upon increasing cohesion between APs, we find a rather abrupt transition from an arch-dominated clogging regime to a cohesion-dominated regime where droplets form at the aperture of the bottleneck. In the arch-dominated regime the flow-rate only weakly depends on the cohesion strength. This suggests that cohesion must not necessarily decrease the group's efficiency passing through geometric constrictions or pores. Such behavior is explained by "slippery" particle bonds which avoids the formation of a rigid particle network and thus prevents clogging. Overall, our results confirm the general applicability of the statistical framework of intermittent flow through bottlenecks developed for granular materials also in case of active microswimmers whose behavior is more complex than that of Brownian particles but which mimic the behavior of living systems.

Two-step nucleation in confined geometry: Phase diagram of finite particles on a lattice gas model.

We use a degenerated Ising model to describe nucleation and crystallization from solution in a confined two-component system. The free energy is calculated using metadynamics simulation with coordination numbers as the reaction coordinates. We deploy nudged elastic band simulation to determine the minimum energy path and give properties of the crystallization path. In this confined system, depletion effects, which could also be caused by slow material transport in the solution, prevent the post-critical cluster from further growth, and the crystalline state would only be stable at larger cluster sizes. Fluctuation of the higher coupling strength of the crystalline state enables further growth until the crystalline cluster is in equilibrium with the solvent, and this way, a second barrier is crossed. From the parameters and setup, we find necessary conditions for the occurrence of two-step nucleation in our system. These findings can be adapted to real systems as biomineralization, colloidal crystallization, and the solidification of metals.

Microscopic diffusion coefficients of dumbbell- and spherocylinder-shaped colloids and their application in simulations of crowded monolayers.

We explore the diffusion properties of colloidal particles with dumbbell and spherocylinder shapes using a hydrodynamic bead-shell approach and additional Brownian dynamics (BD) simulations. By applying the bead-shell method, we determine empirical formulas for the microscopic diffusion coefficients. A comparison of these formulas and established experimental and theoretical results shows remarkable agreement. For example, the maximum relative discrepancy found for dumbbells is less than 5%. As an application example of the empirical formulas, we perform two-dimensional (2D) BD simulations based on a single dumbbell or spherocylinder in a suspension of spheres and calculate the resulting effective long-time diffusion coefficients. The performed BD simulations can be compared to quasi-2D systems such as colloids confined at the interface of two fluids. We find that the effective diffusion coefficient of translation mostly depends on the sphere area fraction ϕ, while the effective diffusion coefficient of rotation is influenced by the aspect ratio and ϕ. Furthermore, the effective rotational diffusion constant seems to depend on the particle shape with the corresponding implementation of the interactions. In the resolution limit of our methods, the shape-dependent differences of the microscopic diffusion coefficients and the long-time diffusion constant of translation are negligible in the first approximation. The determined empirical formulas for the microscopic diffusion coefficients add to the knowledge of the diffusion of anisotropic particles, and they can be used in countless future studies.

Phase behaviour in 2D assemblies of dumbbell-shaped colloids generated under geometrical confinement.

The structure formation and the phase behaviour of monolayers of dumbbell-shaped colloids are explored. For this, we conduct Langmuir-Blodgett experiments at the air/water interface and conventional Brownian dynamic simulations without hydrodynamic interactions. Using Voronoi tessellations and the probability density of the corresponding shape factor of the Voronoi cells p(ζ), the influence of the area fraction φ on the structure of the monolayers is investigated. An increase of the area fraction leads to a higher percentage of domains containing particles with six nearest neighbours and a sharper progression of p(ζ). Especially in dense systems, these domains can consist of aligned particles with uniform Voronoi cells. Thus, the increase of φ enhances the order of the monolayers. Simulations show that a sufficient enhancement of φ also impacts the pair correlation function which develops a substructure in its first maxima. Furthermore, we find that reducing the barrier speed in the Langmuir-Blodgett experiments enhances the final area fraction for a given target surface pressure which, in turn, also increases the percentage of particles with six nearest neighbours and sharpens the progression of p(ζ). Overall, the experiments and simulations show a remarkable qualitative agreement which indicates a versatile way of characterising colloidal monolayers by Brownian dynamics simulations. This opens up perspectives for application to a broad range of nanoparticle-based thin film coatings and devices.

Voltage-Induced Rearrangements in Atomic-Size Contacts.

We study voltage-induced conductance changes of Pb, Au, Al, and Cu atomic contacts. The experiments are performed in vacuum at low temperature using mechanically controllable break junctions. We determine switching histograms, i.e., distribution functions of switching voltages and switching currents, as a function of the conductance. We observe a clear material dependence: Au reveals the highest and almost conductance-independent switching voltage, while Al has the lowest with a pronounced dependence on the conductance. The theoretical study uses density functional theory and a generalized Langevin equation considering the pumping of particular phonon modes. We identify a runaway voltage as the threshold at which the pumping destabilizes the atomic arrangement. We find qualitative agreement between the average switching voltage and the runaway voltage regarding the material and conductance dependence and contact-to-contact variation of the average characteristic voltages, suggesting that the phonon pumping is a relevant mechanism driving the rearrangements in the experimental contacts.

Dynamic ordering of driven spherocylinders in a nonequilibrium suspension of small colloidal spheres.

The ordering effects of driven spherocylinder-shaped rods in a colloidal suspension of small spheres confined to a two-dimensional channel geometry are observed via Brownian dynamics simulations without hydrodynamics. To describe the ordering, an order parameter and an expression for a potential of mean force of an equivalent equilibrium system are defined and analyzed. By varying the application point of the external force along the rods and thus the resulting lever, a transition from a preferred orientation parallel to the direction of the force to a preferred orientation perpendicular to the direction of the force was observed. It is shown that this effect can only be found if the spheres and multiple rods are present. Furthermore, a dependency of the order parameter on the absolute value of the force was discovered. The analysis of the potential of mean force further indicates a transition between two different phases of mean orientation. An observation of the flow equilibrium mean velocity in channel direction led to a s-shaped progression regarding the lever dependency, also marking a transition between two states linked to the mean orientation of the rods. A finite size analysis was conducted. Its results indicate that the transition between the two orientation states is a general phenomenon of the observed rod-sphere mixture.

Stability of nanoparticles in solution: A statistical description of crystallization as a finite particle size effect in a lattice-gas model.

We employ the well-tempered parallel-bias metadynamics algorithm to study the stability of nanoparticles in a lattice gas for crystallization from solution. The model allows us to give a description for the transition from amorphous to crystalline nanoparticles by introducing parameters directly related to the surface tensions of the two phases and also the differences of the entropy per particle in each phase. By examining the parameter space, we find a critical cluster size of crystalline stability, whose temperature and size dependencies follow the Gibbs-Thomson equation. An additional melting point depression due to cluster surface fluctuations is observed, leading to a non-classical nucleation barrier of cluster growth.

Quantized thermal transport in single-atom junctions.

Thermal transport in individual atomic junctions and chains is of great fundamental interest because of the distinctive quantum effects expected to arise in them. By using novel, custom-fabricated, picowatt-resolution calorimetric scanning probes, we measured the thermal conductance of gold and platinum metallic wires down to single-atom junctions. Our work reveals that the thermal conductance of gold single-atom junctions is quantized at room temperature and shows that the Wiedemann-Franz law relating thermal and electrical conductance is satisfied even in single-atom contacts. Furthermore, we quantitatively explain our experimental results within the Landauer framework for quantum thermal transport. The experimental techniques reported here will enable thermal transport studies in atomic and molecular chains, which will be key to investigating numerous fundamental issues that thus far have remained experimentally inaccessible.

Insights from inside the spinodal: Bridging thermalization time scales with smoothed particle hydrodynamics.

We report the influence of the strength of heat bath coupling on the demixing behavior in spinodal decomposing one component liquid-vapor systems. The smoothed particle hydrodynamics (SPH) method with a van der Waals equation of state is used for the simulation. A thermostat for SPH is introduced that is based on the Berendsen thermostat. It controls the strength of heat bath coupling and allows for quenches with exponential temperature decay at a certain thermalization time scale. The present method allows us to bridge several orders of magnitude in the thermalization time scale. The early stage is highly affected by the choice of time scale. A transition from exponential growth to a 1/2 ordinary power law scaling in the characteristic lengths is observed. At high initial temperatures the growth is logarithmic. The comparison with pure thermal simulations reveals latent heat to raise the mean system temperature. Large thermalization time scales and thermal conductivity are figured out to affect a stagnation of heating, which is explained with convective processes. Furthermore, large thermalization time scales are responsible for a stagnation of growth of domains, which is temporally embedded between early and late stage of phase separation. Therefore, it is considered as an intermediate stage. We present an aspect concerning this stage, namely that choosing larger thermalization time scales increases the duration. Moreover, it is observed that diffuse interfaces are formed during this stage, provided that the stage is apparent. We show that the differences in the evolution between pure thermal simulations and simulations with an instantaneously scaled mean temperature can be explained by the thermalization process, since a variation of the time scale allows for the bridging between these cases of limit.

Erratum: Transport and diffusion properties of interacting colloidal particles in two-dimensional microchannels with a periodic potential [Phys. Rev. E 91, 022313 (2015)].

This corrects the article DOI: 10.1103/PhysRevE.91.022313.

Segregation of oppositely driven colloidal particles in hard-walled channels: A finite-size study.

We investigate segregation phenomena of particles driven in opposite directions with Brownian dynamics simulations. The particles interact via a repulsive potential and are confined in three-dimensional hard-walled pipes with quadratic cross sections. In a systematic finite-size study, the pipe length is varied. Ordering on finite length scales can be observed, but global segregation seems to vanish for infinite channel length, as it was recently found for lane formation in two dimensions. As an additional effect of the finite hard-walled boundary conditions, interface vibrations and longitudinal demixing are found.

Effects of temperature on spinodal decomposition and domain growth of liquid-vapor systems with smoothed particle hydrodynamics.

We present a numerical method for simulations of spinodal decomposition of liquid-vapor systems. The results are in excellent agreement with theoretical predictions for all expected time regimes from the initial growth of "homophase fluctuations" up to the inertial hydrodynamics regime. The numerical approach follows a modern formulation of the smoothed particle hydrodynamics method with a van der Waals equation of state and thermal conduction. The dynamics and thermal evolution of instantaneously temperature-quenched systems are investigated. Therefore, we introduce a simple scaling thermostat that allows thermal fluctuations at a constant predicted mean temperature. We find that the initial stage spinodal decomposition is strongly affected by the temperature field. The separated phases react on density changes with a change in temperature. Although, the thermal conduction acts very slowly, thermal deviations are eventually compensated. The domain growth in the late stage of demixing is found to be rather unaffected by thermal fluctuations. We observe a transition from the Lifshitz-Slyozov growth rate with 1/3 exponent to the inertial hydrodynamics regime with a rate of 2/3, only excepted from simulations near the critical point where the liquid droplets are observed to nucleate directly in a spherical shape. The transition between the growth regimes is found to occur earlier for higher initial temperatures. We explain this time dependency with the phase interfaces that become more diffuse and overlap with approaching the critical point. A prolonging behavior of the demixing process is observed and also expected to depend on temperature. It is further found that the observations can excellently explain the growth behavior for pure nonisothermal simulations that are performed without thermostat.

Transport and diffusion properties of interacting colloidal particles in two-dimensional microchannels with a periodic potential.

We report a Brownian dynamics simulation study of a two-dimensional system of repulsive colloidal particles in a channel geometry with a sinusoidal substrate potential under influence of a constant driving. The effect of this driving on the structure, mobility, and diffusion is discussed as well as the appearance of kink and antikink solitons. The competing order principles of the hexagonal crystal structure, the period of the substrate, and the layering due to the confining walls can be either commensurable or incommensurable. The combination of those three leads to new effects. The simultaneous occurrence of kinks and antikinks can be observed, due to the energy difference between boundary- and midlanes, and similarities to the electron-hole conductivity in a semiconductor can be found.

Quantum thermopower of metallic atomic-size contacts at room temperature.

We report conductance and thermopower measurements of metallic atomic-size contacts, namely gold and platinum, using a scanning tunneling microscope (STM) at room temperature. We find that few-atom gold contacts have an average negative thermopower, whereas platinum contacts present a positive thermopower, showing that for both metals, the sign of the thermopower in the nanoscale differs from that of bulk wires. We also find that the magnitude of the thermopower exhibits minima at the maxima of the conductance histogram in the case of gold nanocontacts while for platinum it presents large fluctuations. Tight-binding calculations and Green's function techniques, together with molecular dynamics simulations, show that these observations can be understood in the context of the Landauer-Büttiker picture of coherent transport in atomic-scale wires. In particular, we show that the differences in the thermopower between these two metals are due to the fact that the elastic transport is dominated by the 6s orbitals in the case of gold and by the 5d orbitals in the case of platinum.

Stochastic transport of particles across single barriers.

Transport phenomena of interacting particles are of high interest for many applications in biology and mesoscopic systems. Here we present measurements on colloidal particles, which are confined in narrow channels on a substrate and interact with a barrier, which impedes the motion along the channel. The substrate of the particle is tilted in order for the particles to be driven towards the barrier and, if the energy gained by the tilt is large enough, surpass the barrier by thermal activation. We therefore study the influence of this barrier as well as the influence of particle interaction on the particle transport through such systems. All experiments are supported with Brownian dynamics simulations in order to complement the experiments with tests of a large range of parameter space which cannot be accessed in experiments.