Theory for controlling individual self-propelled micro-swimmers by photon nudging II: confinement.

Photon nudging allows the manipulation and confinement of individual self-propelled micro-swimmers in 2D and 3D environments using feedback controls. Presented in this second part of a two-part contribution are theoretical models that afford the characterization for the positioning distribution associated with active localization. A derivation for the optimal nudging speed and acceptance angle is given for minimal placement uncertainty. The analytical solutions allow for a discussion on the physical underpinning that underlies controllability and optimality.

Theory for controlling individual self-propelled micro-swimmers by photon nudging I: directed transport.

Photon nudging is a new experimental method which enables the force-free manipulation and localization of individual self-propelled artificial micro-swimmers in fluidic environments. It uses a weak laser to stochastically and adaptively turn on and off the swimmer's propulsion when the swimmer, through rotational diffusion, points towards or away from its target, respectively. This contribution presents a theoretical framework for the statistics of both 2D and 3D controls. The main results are: the on- and off-time distributions for the controlling laser, the arrival time statistics for the swimmer to reach a remote target, and how the experimentally accessible control parameters influence the control, e.g., the optimal acceptance angle for directed transport. The results are general in that they are independent of the propulsion or the actuation mechanisms. They provide a concrete physical picture for how a single artificial micro-swimmer could be navigated under thermal fluctuations-insights that could also be useful for understanding biological micro-swimmers.

Exact symmetries in the velocity fluctuations of a hot Brownian swimmer.

Symmetries constrain dynamics. We test this fundamental physical principle, experimentally and by molecular dynamics simulations, for a hot Janus swimmer operating far from thermal equilibrium. Our results establish scalar and vectorial steady-state fluctuation theorems and a thermodynamic uncertainty relation that link the fluctuating particle current to its entropy production at an effective temperature. A Markovian minimal model elucidates the underlying nonequilibrium physics.

Thermo-Osmotic Flow in Thin Films.

We report on the first microscale observation of the velocity field imposed by a nonuniform heat content along the solid-liquid boundary. We determine both radial and vertical velocity components of this thermo-osmotic flow field by tracking single tracer nanoparticles. The measured flow profiles are compared to an approximate analytical theory and to numerical calculations. From the measured slip velocity we deduce the thermo-osmotic coefficient for both bare glass and Pluronic F-127 covered surfaces. The value for Pluronic F-127 agrees well with Soret data for polyethylene glycol, whereas that for glass differs from literature values and indicates the complex boundary layer thermodynamics of glass-water interfaces.

Size dependent efficiency of photophoretic swimmers.

We investigate experimentally the efficiency of self-propelled photophoretic swimmers based on metal-coated polymer particles of different sizes. The metal hemisphere absorbs the incident laser power and converts its energy into heat, which dissipates into the environment. A phoretic surface flow arises from the temperature gradient along the particle surface and drives the particle parallel to its symmetry axis. Scaling the particle size from micro to nanometers, the efficiency of converting optical power into motion is expected to rise with the reciprocal size for ideal swimmers. However, due to the finite size of the metal cap, the efficiency of a real swimmer reveals a maximum depending sensitively on the details of the metal cap shape. We compare the experimental results to numerical simulations.

Single Molecules Trapped by Dynamic Inhomogeneous Temperature Fields.

We demonstrate a single molecule trapping concept that modulates the actual driving force of Brownian motion--the temperature. By spatially and temporally varying the temperature at a plasmonic nanostructure, thermodiffusive drifts are induced that are used to trap single nano-objects. A feedback controlled switching of local temperature fields allows us to confine the motion of a single DNA molecule for minutes and tailoring complex effective trapping potentials. This new type of thermophoretic microbeaker even provides control over a well-defined number of single molecules and is scalable to large arrays of trapping structures.

Stochastic localization of microswimmers by photon nudging.

Force-free trapping and steering of single photophoretically self-propelled Janus-type particles using a feedback mechanism is experimentally demonstrated. Realtime information on particle position and orientation is used to switch the self-propulsion mechanism of the particle optically. The orientational Brownian motion of the particle thereby provides the reorientation mechanism for the microswimmer. The particle size dependence of the photophoretic propulsion velocity reveals that photon nudging provides an increased position accuracy for decreasing particle radius. The explored steering mechanism is suitable for navigation in complex biological environments and in-depth studies of collective swimming effects.