Harnessing Thermal Fluctuations for Purposeful Activities: The Manipulation of Single Micro-swimmers by Adaptive Photon Nudgingy Bian Qian,az Daniel Montiel,a Andreas Bregulla,b Frank Cichos,b and Haw Yang∗a Received Xth XXXXXXXXXX 20XX, Accepted Xth XXXXXXXXX 20XX First published on the web Xth XXXXXXXXXX 20XX DOI: 10.1039/b000000x A simple scheme is presented for remotely maneuvering individual microscopic swimmers by means of on-demand photo-induced actuation, where a laser gently and intermittently pushed the swimmer along its body axis (photon nudging) through a combination of radiation-pressure force and photophoretic pull. The proposed strategy utilized rotational random walks to reorient the micro-swimmer and turned on its propulsion only when the swimmer was aligned with the target location (adaptive control). A Langevin-type equation of motion was formulated, integrating these two ideas to describe the dynamics of the stochastically controlled swimmer. The strategy was examined using computer simulations and illustrated in a proof-of-principle experiment steering a gold-coated Janus micro-sphere moving in three dimensions. The physical parameters relevant to the two actuating forces under the experimental conditions were investigated theoretically and experimentally, revealing that a ∼7 ◦C temperature differential on the micro-swimmer surface could generate a propelling photophoretic strength of ∼0.1 pN. The controllability and positioning error were discussed using both experimental data and Langevin dynamics simulations, where the latter was further used to identify two key unitless control parameters for manipulation accuracy and efficiency; they were the number of random-walk turns the swimmer experienced on the experimental timescale (the revolution number) and the photon-nudge distance within the rotational diffusion time (the propulsion number). A comparison of simulation and experiment indicated that a near-optimal micron-precision motion control was achieved. Introduction is managing the omnipresent thermal fluctuations. The smaller the particle is, the more significant thermal fluc- The capacity to manipulate a single microscopic object, tuations are to the particle's movements; the time it takes navigating it toward its destination and/or along a pro- for the fluctuating forces to move a particle over a dis- grammed path in a liquid environment could have wide- tance of its size scales as its size squared (t / a2). A ranging implications; one might envision such applica- general strategy to overcome the influence of thermal fluc- tions as local surgery of individual living cells, precisely tuations is to introduce external confining potentials. A targeted transport and release of chemicals in cellular celebrated example of this is the laser tweezers, which milieu, and bottom-up assembly of complex micro- and use a very strong laser field to create a trapping poten- nano-structures, to name a few. tial around the particle to restrict the particle's Brown- A major challenge to realizing this overarching vision ian motion; this way, the position of the trapped micro- particle can be changed by translating the laser beam. 1 y Supplementary Information (SI) available: the movie for the trace Using laser tweezers to manipulate small objects, how- shown in Fig. 5; computation simulation details; calculation of the ever, has several drawbacks. For example, laser tweezers radiation-pressure force; reconstruction of the absolute orientation of the particle. See DOI: 10.1039/b000000x/ lack specificity in that any object with sufficient dielectric a 225A Frick Chemistry Laboratory, Princeton University, Prince- contrast against the medium will be trapped. In addition, ton, New Jersey 08544, USA. Fax: +1 609 258 3708; Tel: +1 609 the high laser power tends to result in photo-damage and 258 3578; E-mail: [email protected] heating in the sample. 2 Limitations like these seriously b Molecular Nanophotonics, University of Leipzig, 04103 Leipzig, Germany. confine the scope of laser tweezers for applications in com- z Current address: Mechanical Engineering, Massachusetts Insti- plex environments and living systems. tute of Technology, 77 Massachusetts Avenue, Building3-264, Cam- bridge, Massachusetts 02139 Another example is the anti-Brownian electrokinetic 1{12 j 1 ences all swimmers in the sample at the same time, mak- ing it impossible to steer individual swimmers in an in- dependent fashion. The new concept here is not to forcefully trounce the thermal fluctuations by an external potential but to uti- lize them to reorient and move the swimmer. We imple- ment an adaptive control strategy that is based on the fact that the swimmer propulsion can be regulated so that it is turned on only when the swimmer has the correct orientation towards its target. This enhances the over- all movement in the desired direction relative to those in other directions. This idea is illustrated in Fig. 1a. Even though a swimmer turns randomly, the probabil- Fig. 1 The adaptive photon-nudging idea. (a) Illustration ity for it to be in the correct alignment per unit time is of the algorithm for adaptively steering individual half-metal finite. Therefore, as long as the forced directional move- coated swimmers via laser nudging. The position and dis- ments overcome the random diffusive movements within placements (solid lines), as well as orientations (magenta ar- the time period that the swimmer is aligned, a sequence of rows) of the swimmer are tracked in real time. When the controlled on-and-off actuations will navigate the swim- swimmer orientation aligns with the target (red cross), a laser mer to its destination (cf. Fig. 1b). Consequently, there is beam (green cone) is turned on to propel the swimmer. (b) no need to impose an additional mechanism to steer the Normalized swimmer-target distance, jrj=a, as a function of swimmer rotation; in stead, we let the omnipresent ther- time calculated from the trajectory shown in inset (numerical simulation). (c) Using a sequence of target points, it is pos- mal fluctuations do the work and realign the swimmer sible to steer a micro-swimmer along prescribed paths using towards the target, albeit in a stochastic manner. our adaptive steering strategy (numerical simulation). Photon Nudging To realize our control strategy, a `power engine' that trap, 3 which not only confines the Brownian motion to can be quickly switched on and off is crucial. We rea- a fixed potential, but also introduces a feedback control son that a photo-induced propulsion system could meet to actively reduce the translational Brownian motions. this requirement. Light-induced particle migration has The trapping and steering of nano-objects in this scheme been known for more than a century. This general phe- is, however, restricted to a small volume related to the nomenon can be attributed to two primary mechanisms; electrode structure on the substrate, and is not readily they are radiation pressure 15{17 and photophoresis. 18,19 amenable to manipulation in complex environments. The radiation-pressure force, caused by changes in the Here, we introduce a conceptually new method to steer momentum of photons upon impinging on the particle, is individual micro-objects. This concept is based on re- well understood and is the mechanism for laser trapping. cent efforts in the realization of artificial micro-swimmers The less-well-understood photophoretic effect is believed utilizing a variety of propulsion mechanisms. 4{8 These to be caused by the temperature gradient around a parti- miniaturized man-made swimmers can propel themselves cle due to the uneven light-induced heating of the parti- along their body axis so that, at short times, they ex- cle. Recently, the latter phenomenon has gained renewed hibit directed movements in the lab frame. Due to ro- interests not only for a better understanding of its mech- tational Brownian motion, however, the propelled swim- anism but also for exploring possible applications, 20,21 mers eventually lose track of their traveling direction and though often under the designation of thermophoresis. behave diffusively at long times. The inescapable ther- Historically, however, thermophoresis is not the same as mal fluctuations make it extremely challenging to gener- photophoresis. Photophoresis refers to the particle lo- ate persistently directed motions for self-propelled micro- comotion arising from a temperature asymmetry at the swimmers. Whereas naturally occurring molecular mo- particle created by light whereas thermophoresis refers to tors overcome this difficulty by confining the motion to particle or molecule population migration along a macro- a track, 9 many artificial systems use again an external scopic temperature gradient, e. g., two parallel plates fields to restrict the rotational motion in a controlled maintained at two different temperatures. 22{24 way to maneuver the swimmers to perform complex mo- Photophoresis in general can be attributed to differ- tions. 10{14 In all of these cases the external field influ- ent mechanisms, all related to temperature-dependent 2 j 1{12 interfacial properties such as interfacial tension (the the sphere with the polystyrene first, or with the gold Marangoni forces), the nature of the solute, or the solute coating first. These pieces of information allow us to concentration. In the case of colloids suspended in a solu- understand the manner in which radiation-pressure ac- tion, the major contribution of photophoresis is thought tuation is applied to the Janus particle and to estimate to come from a distortion of the local counter ion cloud the forces it generates. The photon energy absorbed by around the colloidal particle, which has to meet the hy- the gold cap of the Janus particle in turn heats up the drodynamic boundary conditions at the particle surface particle but in an asymmetric way where the gold cap and also at infinity. As a result, an interfacial flow at the hemispherical shell is expected to exhibit a higher tem- particle interface is generated that drives the particle. In- perature than the polystydene particle body does.