Derivation of the Langevin Equation from the Microcanonical Ensemble.

When writing down a Langevin equation for the time evolution of a "system" in contact with a thermal bath, one typically makes the implicit (and often tacit) assumption that the thermal environment is in equilibrium at all times. Here, we take this assumption as a starting point to formulate the problem of a system evolving in contact with a thermal bath from the perspective of the bath, which, since it is in equilibrium, can be described by the microcanonical ensemble. We show that the microcanonical ensemble of the bath, together with the Hamiltonian equations of motion for all the constituents of the bath and system together, give rise to a Langevin equation for the system evolution alone. The friction coefficient turns out to be given in terms of auto-correlation functions of the interaction forces between the bath particles and the system, and the Einstein relation is recovered. Moreover, the connection to the Fokker-Planck equation is established.

Efficiency Fluctuations in Microscopic Machines.

Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a "universal theory of efficiency fluctuations" at long times, for machines with a finite state space, was developed by Verley et al. [Nat. Commun. 5, 4721 (2014)NCAOBW2041-172310.1038/ncomms5721; Phys. Rev. E 90, 052145 (2014)PRESCM1539-375510.1103/PhysRevE.90.052145]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the "universal features" and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two nontrivial models of colloidal engines.

Mechanical chiral resolution.

Mechanical interactions of chiral objects with their environment are well-established at the macroscale, like a propeller on a plane or a rudder on a boat. At the colloidal scale and smaller, however, such interactions are often not considered or deemed irrelevant due to Brownian motion. As we will show in this tutorial review, mechanical interactions do have significant effects on chiral objects at all scales, and can be induced using shearing surfaces, collisions with walls or repetitive microstructures, fluid flows, or by applying electrical or optical forces. Achieving chiral resolution by mechanical means is very promising in the field of soft matter and to industry, but has not received much attention so far.

DNA dielectrophoresis: Theory and applications a review.

Dielectrophoresis is the migration of an electrically polarizable particle in an inhomogeneous electric field. This migration can be exploited for several applications with (bio)molecules or cells. Dielectrophoresis is a noninvasive technique; therefore, it is very convenient for (selective) manipulation of (bio)molecules or cells. In this review, we will focus on DNA dielectrophoresis as this technique offers several advantages in trapping and immobilization, separation and purification, and analysis of DNA molecules. We present and discuss the underlying theory of the most important forces that have to be considered for applications with dielectrophoresis. Moreover, a review of DNA dielectrophoresis applications is provided to present the state-of-the-art and to offer the reader a perspective of the advances and current limitations of DNA dielectrophoresis.

Driven Anisotropic Diffusion at Boundaries: Noise Rectification and Particle Sorting.

We study the diffusive dynamics of a Brownian particle in the proximity of a flat surface under nonequilibrium conditions, which are created by an anisotropic thermal environment with different temperatures being active along distinct spatial directions. By presenting the exact time-dependent solution of the Fokker-Planck equation for this problem, we demonstrate that the interplay between anisotropic diffusion and hard-core interaction with the plain wall rectifies the thermal fluctuations and induces directed particle transport parallel to the surface, without any deterministic forces being applied in that direction. Based on current micromanipulation technologies, we suggest a concrete experimental setup to observe this novel noise-induced transport mechanism. We furthermore show that it is sensitive to particle characteristics, such that this setup can be used for sorting particles of different sizes.

Direct measurement of thermophoretic forces.

We study the thermophoretic motion of a micron sized single colloidal particle in front of a flat wall by evanescent light scattering. To quantify thermophoretic effects we analyse the nonequilibrium steady state (NESS) of the particle in a constant temperature gradient perpendicular to the confining walls. We propose to determine thermophoretic forces from a "generalized potential" associated with the probability distribution of the particle position in the NESS. Experimentally we demonstrate, how this spatial probability distribution is measured and how thermophoretic forces can be extracted with 10 fN resolution. By varying temperature gradient and ambient temperature, the temperature dependence of Soret coefficient ST(T) is determined for r = 2.5 µm polystyrene and r = 1.35 µm melamine particles. The functional form of ST(T) is in good agreement with findings for smaller colloids. In addition, we measure and discuss hydrodynamic effects in the confined geometry. The theoretical and experimental technique proposed here extends thermophoresis measurements to so far inaccessible particle sizes and particle solvent combinations.

Motility of an autonomous protein-based artificial motor that operates via a burnt-bridge principle.

Inspired by biology, great progress has been made in creating artificial molecular motors. However, the dream of harnessing proteins - the building blocks selected by nature - to design autonomous motors has so far remained elusive. Here we report the synthesis and characterization of the Lawnmower, an autonomous, protein-based artificial molecular motor comprised of a spherical hub decorated with proteases. Its "burnt-bridge" motion is directed by cleavage of a peptide lawn, promoting motion towards unvisited substrate. We find that Lawnmowers exhibit directional motion with average speeds of up to 80 nm/s, comparable to biological motors. By selectively patterning the peptide lawn on microfabricated tracks, we furthermore show that the Lawnmower is capable of track-guided motion. Our work opens an avenue towards nanotechnology applications of artificial protein motors.

Circular motion of asymmetric self-propelling particles.

Micron-sized self-propelled (active) particles can be considered as model systems for characterizing more complex biological organisms like swimming bacteria or motile cells. We produce asymmetric microswimmers by soft lithography and study their circular motion on a substrate and near channel boundaries. Our experimental observations are in full agreement with a theory of Brownian dynamics for asymmetric self-propelled particles, which couples their translational and orientational motion.

Separation of chiral particles in micro- or nanofluidic channels.

We propose a method to separate enantiomers in microfluidic or nanofluidic channels. It requires flow profiles that break chiral symmetry and have regions with high local shear. Such profiles can be generated in channels confined by walls with different hydrodynamic boundary conditions (e.g., slip lengths). Because of a nonlinear hydrodynamic effect, particles with different chirality migrate at different speeds and can be separated. The mechanism is demonstrated by computer simulations. We investigate the influence of thermal fluctuations (i.e., the Péclet number) and show that the effect disappears in the linear response regime. The details of the microscopic flow are important and determine which volume forces are necessary to achieve separation.

Anomalous thermodynamics at the microscale.

Particle motion at the microscale is an incessant tug-of-war between thermal fluctuations and applied forces on one side and the strong resistance exerted by fluid viscosity on the other. Friction is so strong that completely neglecting inertia--the overdamped approximation--gives an excellent effective description of the actual particle mechanics. In sharp contrast to this result, here we show that the overdamped approximation dramatically fails when thermodynamic quantities such as the entropy production in the environment are considered, in the presence of temperature gradients. In the limit of vanishingly small, yet finite, inertia, we find that the entropy production is dominated by a contribution that is anomalous, i.e., has no counterpart in the overdamped approximation. This phenomenon, which we call an entropic anomaly, is due to a symmetry breaking that occurs when moving to the small, finite inertia limit. Anomalous entropy production is traced back to futile phase-space cyclic trajectories displaying a fast downgradient sweep followed by a slow upgradient return to the original position.

Chiral particle separation by a nonchiral microlattice.

We conceived a model experiment for a continuous separation strategy of chiral molecules (enantiomers) without the need of any chiral selector structure or derivatization agents: Microparticles that only differ by their chirality are shown to migrate along different directions when driven by a steady fluid flow through a square lattice of cylindrical posts. In accordance with our numerical predictions, the transport directions of the enantiomers depend very sensitively on the orientation of the lattice relative to the fluid flow.

Brownian dynamics simulations with hard-body interactions: spherical particles.

A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian particle on a one-dimensional half-line. The motion of a Brownian particle is decomposed into a component that is affected by hard-body interactions and into components that are unaffected. The hard-body interactions are incorporated by replacing the "affected" component of motion by the evolution on a half-line. It is discussed under which circumstances this approach is justified. In particular, the algorithm is developed and formulated for systems with space-fixed obstacles and for systems comprising spherical particles. The validity and justification of the algorithm is investigated numerically by looking at exemplary model systems of soft matter, namely at colloids in flow fields and at protein interactions. Furthermore, a thorough discussion of properties of other heuristic algorithms is carried out.

Electrodeless dielectrophoresis for bioanalysis: theory, devices and applications.

Dielectrophoresis is a non-destructive, label-free method to manipulate and separate (bio-) particles and macromolecules. The mechanism is based on the movement of polarizable objects in an inhomogeneous electric field. Here, microfluidic devices are reviewed that generate those inhomogeneous electric fields with insulating posts or constrictions, an approach called electrodeless or insulator-based dielectrophoresis. Possible advantages compared to electrode-based designs are a less complex, monolithic fabrication process with low-cost polymeric substrates and no metal surface deterioration within the area of sample analysis. The electrodeless design has led to novel devices, implementing the functionality directly into the channel geometry and covering many areas of bioanalysis, like manipulation and separation of particles, cells, DNA, and proteins.

Brownian motion: absolute negative particle mobility.

Noise effects in technological applications, far from being a nuisance, can be exploited with advantage - for example, unavoidable thermal fluctuations have found application in the transport and sorting of colloidal particles and biomolecules. Here we use a microfluidic system to demonstrate a paradoxical migration mechanism in which particles always move in a direction opposite to the net acting force ('absolute negative mobility') as a result of an interplay between thermal noise, a periodic and symmetric microstructure, and a biased alternating-current electric field. This counterintuitive phenomenon could be used for bioanalytical purposes, for example in the separation and fractionation of colloids, biological molecules and cells.

Dielectrophoretic trapping and polarizability of DNA: the role of spatial conformation.

Dielectrophoresis is a convenient tool for controlled manipulation of DNA with numerous applications, including DNA trapping, stretching, and separation. However, the mechanisms behind the dielectrophoretic properties of DNA are still under debate, and the role of conformation has not been addressed yet. Here, we quantify dielectrophoretic effects on DNA by determining its polarizability from microfluidic single molecule trapping experiments. We systematically study different DNA configurations (linear and supercoiled, 6-164 kbp) and demonstrate that the polarizability strongly depends on the specific conformation and size of the DNA molecules. The connection to its spatial extension is established by measuring diffusion coefficients and from that the radii of gyration; details about the spatial DNA structure are obtained from atomic force microscopy images. For linear and supercoiled DNA fragments, we found a power-law scaling for the polarizabilities and the diffusion coefficients. Our results imply a scaling of the polarizability with the radius of gyration, alpha approximately Rg0.9+/-0.1 and alpha approximately Rg1.6+/-0.2 for linear and supercoiled DNA, respectively. As an application, we demonstrate the separation of DNA topoisomers based on their dielectrophoretic properties, achieving baseline resolution within 210 s. Purified DNA samples of specific configuration may be of great importance for DNA nanoassembly or future DNA vaccines.

Microfluidic sorting of stereoisomers.

Isomeric molecules that only differ in the spatial orientation of their constituents are called stereoisomers. We demonstrate that different stereoisomers are transported typically at different velocities in a fluid streaming through a straight microchannel. As the underlying mechanism, we identify a translation-rotation coupling in the motion of the molecules which is specific for the molecule structure. This effect can be exploited for the separation of stereoisomers, a task of immense importance in biotechnology and pharmaceutics.

Exploiting lattice potentials for sorting chiral particles.

Several ways are demonstrated of how periodic potentials can be exploited for sorting molecules or other small objects which only differ by their chirality. With the help of a static bias force, the two chiral partners can be made to move along orthogonal directions. Time-periodic external forces even lead to motion into exactly opposite directions.

Measurement of anomalous diffusion using recurrent neural networks.

Anomalous diffusion occurs in many physical and biological phenomena, when the growth of the mean squared displacement (MSD) with time has an exponent different from one. We show that recurrent neural networks (RNNs) can efficiently characterize anomalous diffusion by determining the exponent from a single short trajectory, outperforming the standard estimation based on the MSD when the available data points are limited, as is often the case in experiments. Furthermore, the RNNs can handle more complex tasks where there are no standard approaches, such as determining the anomalous diffusion exponent from a trajectory sampled at irregular times, and estimating the switching time and anomalous diffusion exponents of an intermittent system that switches between different kinds of anomalous diffusion. We validate our method on experimental data obtained from subdiffusive colloids trapped in speckle light fields and superdiffusive microswimmers.

Diffusion of colloidal particles in a tilted periodic potential: theory versus experiment.

We investigate the diffusion of a colloidal particle in a tilted periodic potential created by means of ten rotating optical tweezers arranged on a circle. Because of the viscous drag, the trap rotation leads to the onset of a tilting force in the corotating reference frame, so that in that frame the system can be described as an overdamped Brownian particle in a tilted periodic potential. The excellent agreement of the velocity and diffusion coefficient as a function of rotating frequency with theoretical predictions allowed us to extract the main parameters characterizing the system--the coefficient of free thermal diffusion and the potential corrugation depth--from the experimental results.

Transient chaos induces anomalous transport properties of an underdamped Brownian particle.

For an underdamped Brownian particle in a one-dimensional periodic potential we theoretically predict three unusual transport properties: (i) A static bias force (of either sign) generates an average particle motion in the opposite direction. (ii) A small bias leads to a particle transport in the direction of the bias, but upon increasing the bias the particle velocity reverses direction. (iii) For a given bias force, the particle motion follows the direction of the force for low temperatures, but upon increasing the temperature reverses its direction. The considered model is shown to be minimal for the occurrence of these phenomena. A detailed analysis of its deterministic properties and the influence of thermal noise is carried out with numerical simulations that are complemented by analytical approximations. Intuitive explanations of the basic mechanism behind the three effects are provided; their origin is attributed to a subtle interplay between the stability of coexisting attractors, noise induced metastability, and transient chaos. An experimental system for the realization of the predicted effects is given within the Stewart-McCumber model for Josephson junctions. Suitable parameter values for which these effects can be observed are quite realistic experimentally.