A Path toward Inherently Asymmetric Micromotors

Since the highly cited paper by Purcell postulating the “Scallop theorem” almost 50 years ago, asymmetry is an unavoidable part of micromotors. It is frequently induced by self‐shadowing or self‐masking, resulting in so‐called Janus colloids. This strategy works very reliably, but turns into a bottleneck once up‐scaling becomes important. Herein, existing alternatives are discussed and a novel synthetic pathway yielding active swimmers in a one‐pot synthesis is presented. To understand the resulting mobility from a single material, the geometric asymmetry is evaluated using a python based algorithm and this process is automated in an open access tool.


Introduction
Motion on the small scale is dominated by physics characterized by a few dimensionless numbers, with the most prominent one being the Reynolds number (Re). Named after engineer Oswald Reynolds, Re is defined as the ratio of viscous to inertial forces and calculated via where ρ is the density, u is the speed of the object, L is its length, and μ is the viscosity. The effects of a low Reynolds number on motion have been investigated by physicists for almost a century now, starting from Lighthill, who defined the concept of a "squirming" motion. He modeled the fluid mathematically as prescribed surface velocities on a continuous spherical surface. [1] Almost two decades later, Blake adapted and refined Lighthill's model to describe the effect of cilia actuation of the ciliate Paramecium. [2] Improved microscopy facilities and the surge of knowledge strengthened the general interest in nano-and microscale active matter on both, artificial and biological grounds. The different approaches to achieving motility on the small scale did not remain unobserved and so in 1977 Purcell explained in a much-cited article how time irreversibility arises from the Navier-Stokes equations and the microorganisms' need for asymmetry independent of the arrow of time. [3] The limitations of the scallop theorem for the creation of microswimmers were probed by a team around Peer Fischer, by creating a single-hinge microswimmer able to propel in non-Newtonian liquids. [4] In comparison, most biological microswimmers achieve sufficient asymmetry through distinct flagellar motion, specifically rotation in case of bacteria, while ciliates, many algae, and sperm rely on asymmetric bending strategies. [5] These motion strategies are often accompanied by elongated morphologies, that lead to clear behavioral consequences in many specific circumstances and conditions, for example, the weather vane mechanism for rheotaxis. [6] Biological swimmers were long believed to be hard to control, but it was recently demonstrated that they can be optically manipulated. [7,8] A large part of artificial microswimmers rely on phoretic mechanisms to achieve self-propulsion, that is, the formation of asymmetric gradients that interact with the particle surface and cause propulsion.
The probably most common strategy to break the symmetry is the Janus geometry, involving either an active and an inert hemisphere [9] or two halves contributing differently to the chemical reaction [10] and thereby fostering an asymmetric product gradient. Janus particles can be fabricated in different ways and are open to a multitude of material combinations. The fabrication process consists of three steps: commonly, a (spherical) base particle is either synthesized or commercially obtained. The crucial step is then to shield one hemisphere of the particle so that the catalyst, cocatalyst, or passivating material is not deposited over its whole surface. Coating a metal on a monolayer of particles can then be achieved by different methods such as thermal or electroor electron-beam deposition. While this method has produced many successfully moving microswimmers, it also bears substantial drawbacks: the necessity to shield one hemisphere of the particles presents a bottleneck to the amount of swimmers that can be produced at once, as only a limited number can be deposited in a monolayer or coated with a polymer while keeping a high sample quality and uniformity. The swimmer yield can of course be scaled up by producing multiple batches, but this in turn prolongs an already excessive multistep process and reproducibility is often hard to achieve with these methods. This has led to severely different values of microswimmer speed for particles of the same materials and dimensions, a phenomenon very pronounced for Au@TiO 2 -based swimmers. [10,11] DOI: 10.1002/aisy.202200091 Since the highly cited paper by Purcell postulating the "Scallop theorem" almost 50 years ago, asymmetry is an unavoidable part of micromotors. It is frequently induced by self-shadowing or self-masking, resulting in so-called Janus colloids. This strategy works very reliably, but turns into a bottleneck once up-scaling becomes important. Herein, existing alternatives are discussed and a novel synthetic pathway yielding active swimmers in a one-pot synthesis is presented. To understand the resulting mobility from a single material, the geometric asymmetry is evaluated using a python based algorithm and this process is automated in an open access tool.
Among the broad range of semiconducting photocatalytic materials, TiO 2 has emerged as one of the most widely used photocatalysts inside and outside of active matter, due to its low cost, high photoactivity, physical and chemical robustness, and low environmental toxicity. [12] Methods for synthesizing spherical TiO 2 particles ranging from the nano-to the microscale are abundant, [13,14] but for spherical particles on a solid substrate and illuminating from below, the shadow effect is usually not sufficient to induce active motion. [15] Chen et al. were able to control the motion of isotropic microparticles by changing the position of the UV light source. [16] In addition to these few approaches, most micromotors still require asymmetrization using typical deposition methods that require monolayer fabrication. [17] A process that still leads to Janus particles, but increases the scalability to a certain extent, is the asymmetric modification of particles via electrochemistry. [18] Researchers have been seeking approaches to simplify the fabrication process of catalytic microswimmers with the aim to find new sources of asymmetry that do not need to be introduced in a multistep process. Ideally, batch size and reproducibility of the systems should increase at the same time. Alternative methods for the creation of isotropic particles have led to approaches based on surfactant-induced dewetting. [19,20] More recently, Zhu et al. have partially encapsulated photocatalytic TiO 2 or ZnO colloids with polysiloxane, reducing the fabrication process of the microswimmers to a two-step one. [21] Further, inherently phase asymmetric spherical TiO 2 photocatalytic micromotors move based on random asymmetric product distribution. [22] A very scalable approach was followed by the group of Peer Fischer, using commercial titanium dioxide powder, consistent of particles with irregular shape. While the individual particle motion was not studied in detail (due to the random shapes), highly interesting collective interactions resulted from the synergy of larger numbers. [23] Another elegant particle design relied on the asymmetric distribution of charge carriers in BiVO 4 upon irradiation. Heckel et al. developed bismuth vanadate particles in squareshaped, [24,25] spheroidal, [26] and single-crystalline [27] geometries that exhibit motility and active assembly without any asymmetrization step because of their intrinsic crystal properties. This strategy is transferable only to materials with significantly different band structures of exposed crystal facets, for example, for TiO 2 semiconductors, conferring this type of asymmetry has not yet been achieved. [28] For more flexibility in material choices, modular approaches have been developed in experimental [29,30] and theoretical systems. [31] Also widely usable without specific material constraints is the strategy followed by the Cichos group, combining asymmetric irradiation, and completely symmetric particles. [32] While the necessity of production up-scaling is true for all types of active matter, many attempts have been made especially for photocatalytic microswimmers utilizing light as energy source. Light offers unique advantages like wireless control, reversible switching (on/off state), and precise energy management. [33,34] Photocatalytic micromotors are based on photoactive materials, which are excited with a particular wavelength of light resulting in charge separation (electron-hole pair generation) and simultaneous redox reactions with the surrounding reactants. [11] Geometrical asymmetrization within a micromotor can also lead to enhanced ballistic motion and is a much needed approach in the development of scalable, inherently asymmetric micromotors. Approaches where synthetic routes result in asymmetric morphologies have been presented, but are rare. [35] 1.1. Development of Inherently Asymmetric TiO 2 : Pac-Man Structure Here, we investigate a solvothermal approach for the synthesis of Pac-Man-like TiO 2 structures, providing a scalable approach toward geometric asymmetry. This porous Pac-Man structure is obtained due to a pressure-driven evaporation process, displayed in Figure 1A. [36] In the initial step, the TiO 2 precursor titanium butoxide is dissolved with a polymeric surfactant (poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock copolymer) in an acidic tetrahydrofuran (THF) solution, followed by the formation of a monomicellar gel after removal of THF. At higher temperatures, these small micelles assemble into larger spherical aggregates incorporated with residual solvents. During the solvothermal treatment, the solvent vapors create a gradually increasing interior pressure within the particles, and once it overcomes the exterior solvothermal pressure, partial cracks are formed to release the accumulated stress (see Figure 1A). The porosity of the formed Pac-Man TiO 2 particles is characterized morphologically and with nitrogen adsorption measurements (see Section S2, Supporting Information).
The cracks are thus formed before the calcination step providing the required geometrical asymmetrization. To evaluate the extent of this morphological imbalance, we adapted a simple evaluation method [37] that we have already used for ZnO yolk shell geometries (see Figure 1A, scanning electron microscope [SEM] image) [35] and we developed a software to assist with the characterization. The SEM image of a typical Pac-Man particle was symmetrically dissected into two lobes and the linear distance with respect to the reference line (left) from the same point is measured. The particle is isometrically different at the center due to the formed crack. To facilitate the adaptation of this method, we created a simple python-based algorithm, to load and analyze images, defining an asymmetry factor α. The methodology is described in more detail in the methods section, while the code is made available. The resulting TiO 2 particles show this cracked architecture before ( Figure 1B) the calcination step and maintain this structure after calcination ( Figure 1C). Thus, this synthesis route is very effective in forming geometrically asymmetric TiO 2 particles. The overall size distribution curve of the synthesized TiO 2 particles (both uncalcined and calcined) is shown in Figure 1D with an average size of 2.65 AE 0.4 μm. A single synthesis yields around 0.5 g of product and is easily scalable, a clear advantage compared to the low yields in our ZnO yolk-shell particles, resulting in few milligram of particles. [35] Further morphological comparison and individual particle diameters at each calcination step are detailed in Supporting Information ( Figure S2 and Table S1 in Section S3, Supporting Information).
Although the geometrical asymmetrization is a requirement for achieving a product gradient that leads to active motion, the crystalline properties are crucial for photocatalytic activity. The crystal structure is routinely characterized by a powder X-ray diffractometer evaluating diffraction reflexes. The uncalcined sample shows a rutile phase with low crystallinity www.advancedsciencenews.com www.advintellsyst.com indicating the formation of the rutile phase during the hydrothermal step (see Figure 2A). The comparison with the calcinated product shows that no phase transition happens during the annealing step, the calcination merely produces a higher degree of crystallinity in TiO 2 particles, indicated by decreased peak widths, enabling the particles to function as an efficient photocatalyst. The crystal properties directly affect the interaction properties of a particle with light. To identify the wavelength corresponding to the bandgap of the material, we studied the absorption spectra of both uncalcined and calcined TiO 2 particles using a UV-vis diffuse reflectance spectroscopy (DRS) spectrophotometer.
Both the samples have similar bandgaps (E g ) of 3.09 eV for uncalcined and 3.03 eV for calcined TiO 2 , which lie within the expected range for conventional rutile TiO 2 (see inset Figure 2B). [38]

Motion of Pac-Man TiO 2 Microparticles
Artificial micro/nanomotors are characterized by autonomous motion, which is attained by constantly translating energy (chemical, optical, acoustic, magnetic, electric, etc.) to mechanical work (propulsion). [33] We and others showed earlier [15,39,40] that simple, spherical TiO 2 particles show activity, but due to a lack of Figure 1. A) Scheme displaying the synthesis strategy, asymmetry characterization following Choi. [37] Scanning electron microscope (SEM) images of B) uncalcined C) calcined TiO 2 microparticles with yellow spheres showing the cracked particles and the green depicting the probable or uncracked ones. D) Size distribution graph showing the average particle diameter (including both uncalcined and calcined ones). Scale bar: 1 μm. www.advancedsciencenews.com www.advintellsyst.com asymmetry, no significant motility is observed. Here, the motion of Pac-Man particles was studied in diluted peroxide solutions and under UV illumination. While the exact localization of the half reactions is unknown and also the swimming position can only be insinuated from optical microscopy (see Supporting Information and Videos S4 and S5, Supporting Information), we conjecture the photochemical reactions associated with the active behavior to be as represented in Figure 3A: when UV light irradiates the particles, the electron-hole pair is generated and both charge carriers diffuse to the surface, where simultaneous redox reactions with the H 2 O 2 fuel happen. The resulting gradients create fluid flows that move the particles forward. It is difficult to evaluate whether the rate of reaction is higher at the inner or outer surfaces and how the geometric constraints affect the force generations. However, as can be seen in the videos, Supporting Information, we observed several instances where the shape asymmetry was visible and the particle orientation can be estimated. We recognize that the exact swimming orientation and mechanism need to be validated by 3D particle tracking velocimetry, but this is beyond the scope of this paper. For now, we simply observe that due to the geometrical anisotropy of these particles and different reaction rates on the particle surface (due to geometry and shadow effects), a directed motion is generated. The instantaneous speed of a calcined micromotor under UV off-on state is shown in Figure 3B (5 wt% H 2 O 2 , 3.68 W cm À2 UV intensity). The micromotor was tracked over 4 UV off-on cycles demonstrating a quick and precise photoresponse with reversible switching states. The time-lapse motion of these particles in the absence and presence of UV is shown in Supporting Information ( Figure S4 and Video S4). As expected from their low crystallinities, the uncalcined particles show weak propulsion and increasing the UV intensity does not affect their swimming speed significantly (see Figure 3C red box plots).
The calcined particles, in contrast, propel autonomously and the propulsion is proportional to the incident UV light intensity (see Figure 3C blue box plots, and Videos S1 and S2, Supporting Information). Additionally, the swimming speed also scales with the fuel concentration (see Section S4 and Video S3, Supporting Information). The motion of the calcined particles is primarily caused by the acquired catalytic activity during the annealing step, enabling the particle to efficiently degrade hydrogen peroxide. The gradients used for propulsion are due to the Pac-Man-like crack and although the uncalcined particles are morphologically similar, their poor photoactivity does not lead to ballistic motion. We can rule out that a phase distribution contributes to the asymmetrization because in the X-ray diffraction (XRD), it is evident that our particles consist of a pure rutile phase. [22]

Conclusion
To conclude, we confirm that two factors are relevant for obtaining active, directed mobility: (photo)catalytic activity in combination with a structural asymmetry. Using a one-pot synthesis to obtain Pac-Man structured rutile TiO 2 particles, we find that the uncalcined particles, even though already consisting of a crystalline rutile phase, do not show active motion. The broader peaks in XRD powder diffraction indicate smaller crystal sizes, which offer plenty of recombination sites, so that few charge carriers reach the surface to induce chemical H 2 O 2 degradation. Only the asymmetric structures obtained after calcination show sufficient crystallinity, so that both requirements for active matter are fulfilled.
Material Characterization: XRD reflexes were obtained using Bruker 2D phaser powder X-ray diffractometer (Germany) using Cu Kα radiation (30 kV, 10 mA). Nitrogen adsorption and desorption measurements were conducted using Nova3000e from Quantachrome at standard temperature (77 K) and pressure (1 atm) (STP) to determine the specific surface area, pore diameter, total pore volume, and pore size distribution. Prior measurements of the sample were degassed at 180°C for 20 h. The morphology of as-synthesized TiO 2 particles were characterized via SEM using a Hitachi FESEM SU8020 (2 kV, 10 mA). Using Fiji (ImageJ) software, the www.advancedsciencenews.com www.advintellsyst.com diameter of over 300 particles (including both uncalcined and calcined TiO 2 particles) was evaluated and the size distribution histogram was plotted. UV-visible DRS was acquired for colloidal solution of the samples in water using a Cary 5000 UV-vis-NIR spectrophotometer. Motion experiments were recorded using a Zeiss camera (Axiocam 702 Mono) attached to an inverted microscope (Axio observer from Carl Zeiss Microscopy GmbH). The samples were illuminated with 385 nm ultraviolet-light-emitting diode (UV LED) obtained from a flexible Colibri 7 light source. The operating UV intensities were 1.93, 3.68, and 9.49 W cm À2 . [41] The frame rate of the videos was 40 fps and it was finally evaluated and analyzed using Fiji (ImageJ) and MATLAB. Synthesis of Porous Pac-Man-like TiO 2 : The synthesis protocol was adapted following Lan et al. [36] Typically in a beaker containing 1.6 g of Pluronic P123, 30 mL of THF was added, followed by addition of 2 mL CH 3 COOH, and 3 mL of HCl. The solution was stirred until the polymer completely dissolves. TBOT of 3 mL was added dropwise at a rate of 18 mL h À1 to the aforementioned stirring mixture using a mechanical syringe pump, followed by subsequent addition of 200 μL DI water. The mixture was further stirred for 10 more minutes to obtain a golden yellow solution. It was then heated at 40°C for 24 h to obtain a transparent light yellow gel. The gel of 2 g was weighed on a 50 mL teflon vessel, and autoclaved at 70°C for 24 h. A white precipitate was obtained which was repeatedly washed with methanol and dried at 70°C overnight. Part of the obtained sample was used for motion and other characterization (mentioned as "uncalcined"), the other part of the sample was further calcined first at 350°C for 3 h under N 2 and then in air at 400°C for 3 h (mentioned as "calcined").
Motion Characterization: A very diluted solution of uncalcined and calcined TiO 2 samples in DI water were studied in an inverted microscope setup at different light intensities and peroxide concentrations.
Asymmetry evaluation code of the python script let a user load a Pac-Man-like image and mark a vertical line as central reference. The user manually marked points in the left hemisphere's border that were used as reference for points in the right hemisphere. After a reference point was marked, the program limited the user to mark a corresponding point in the same horizontal line in the opposite side. The ratio of distances from each point pair to the central vertical line was displayed next to the right hemisphere point, as shown in Figure 1A, SEM image. The program displayed the average of ratios as the asymmetry factor α, and let the user reposition the vertical central reference whenever wanted.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.