Boundaries can steer active Janus spheres

The advent of autonomous self-propulsion has instigated research towards making colloidal machines that can deliver mechanical work in the form of transport, and other functions such as sensing and cleaning. While much progress has been made in the last 10 years on various mechanisms to generate self-propulsion, the ability to steer self-propelled colloidal devices has so far been much more limited. A critical barrier in increasing the impact of such motors is in directing their motion against the Brownian rotation, which randomizes particle orientations. In this context, here we report directed motion of a specific class of catalytic motors when moving in close proximity to solid surfaces. This is achieved through active quenching of their Brownian rotation by constraining it in a rotational well, caused not by equilibrium, but by hydrodynamic effects. We demonstrate how combining these geometric constraints can be utilized to steer these active colloids along arbitrary trajectories.

Supplementary Table 2 Supplementary Table 2: Measured values of zeta potential of the Janus particle, platinum and polystyrene halves of the Janus particle in water and 5% H 2 O 2 at time 10 mins and 60 mins. This table shows the actual values of the zeta potential measured for each particle and the averages for each trial, referenced in Figure 3g of the manuscript. The averages indicate very good consistency within a batch and the intra-batch variability is similar for trials with and without H 2 O 2 . Thus it is  reducing propulsion velocity and increasing particle size will require a greater cant angle to overcome sedimentation, and that also for sufficiently large colloids, sedimentation will become inevitable, as due to the (1/a) dependency on propulsion velocity there will not be sufficient force to overcome sedimentation irrespective of ϴ. To illustrate this experimentally, we investigated some a=5 µm colloids, and found that for low fuel concentrations (approximately 1.5 %), sedimentation from the top surface was observed.

Supplementary Note 2: Exploring the limits for boundary steering phenomena
For boundary steering to be exploited for applications, it is important that active colloids retain the ability to be directed or confined at boundaries for sufficient durations to enable transport over useful distances. Encouragingly in this context, during our experiments, which involved repeated observations of hundreds of randomly selected particles for periods of several minutes, we observed very few cases where a particle would detach from a planar interface, or cease to be steered by a multi-planar geometry. Indeed we have shown that as a result micron sized active colloids can be steered by boundaries over macroscopic cm length scales. Because of this persistence of motion it is experimentally difficult to investigate the frequency of "detachment" events where active colloids remove from a boundary or a plane. However, by inspection it appears that the residence time for a given active colloid will depend on the degree of rotational confinement, and the consequences of temporary misalignment. Our theoretical analysis and experimental data has indicated that at slower propulsion speeds rotational quenching is diminished, and so we can expect a higher frequency of events where the active colloid is no longer completely orientated parallel to the nearby interfaces. Therefore we may predict lower residence times for slower moving particles.
However, it is also clear that momentary misalignment may not necessarily lead to a particle separating from the interface. In some cases the misalignment may cause the propulsion vector to point towards the solid interface, which may not lead to detachment. Even if the propulsion vector is orientated away from the steering/confining interfaces, this may not generate sufficient force to 9 result in the active colloid returning to "bulk". This specifics of this case will depend on the geometry and size of the colloid, for example, for a colloid to leave the lower planar surface of a container will require it to produce sufficient upwards propulsion velocity to overcome its tendency to sediment, a factor that will actually encourage low velocity colloids to remain at the surface despite more frequent misalignments. Another consideration is stochastic variations in distance of the colloid from the constraining interface. Our theoretical analysis shows that the pre-factor determining the strength of orientational quenching has an inverse cubic relationship with separation from the wall. This leads to the possibility of Brownian "kicks" randomly translating the active colloid sufficiently far from the interface that orientational quenching is no longer experienced. Our experiments confirm that these events do not happen frequently at the sizes we have investigated. However, this effect could become limiting at smaller colloidal sizes, as Brownian translational diffusion rate increases.
While this general discussion applies to all the geometries considered, we also present a more detailed consideration of the differences between the single plane active colloid arrangement which we subjected to rigorous analysis, and the multi-plane arrangements. It was our hypothesis that adding an additional plane or planes beyond the single plane system would display the same hydrodynamic confinement phenomena, however now with additional axis of rotation being quenched, resulting in boundary steering. In comparison to the single planar system, the arguments we developed for hydrodynamic rotational confinement being a dominant factor in the system remain valid: the substrate material was unchanged for experiments conducted at an "edge", and silicon substrates were used for the groove experiments which have also similar properties.
Consequently the electrostatic interactions are expected to stay the same. We observed that all sized particles moving within ten percent hydrogen peroxide solutions experienced prolonged boundary steering with long residence times at the edge formed between either the upper or lower planar cuvette surface and the vertical cuvette sidewall. This steering effect also tolerated the moderate curvature of the steering boundary found at the corners of the cuvette. As reported for the single plane case, the fluorescence intensity of the active colloid remained unchanged during confinement, and a constant "phase of the moon" was observed following the boundary direction and correlating with the expected propulsion direction away from the platinum cap. This shows that the boundary steering did correlate with the active colloid orientation confinement relative to both planes. For the case of the grooved lithographic example, the additional constraint that the colloid could physically fit within the groove was imposed, which in practise resulted in active colloids of a given size entering grooves that were approximately 2 µm wider than their diameters. Due to optical reflections within the groove, it was not possible to determine the orientation of the active colloid as it followed a groove, however persistent propulsion motion along the groove was observed until the colloid reached the end at which point it became stuck. At this point microscopy did allow the orientation of the colloid to be viewed, and this was found to be aligned as expected relative to both boundaries. As mentioned in the main text, the groove system possesses the potential to prevent Brownian kicks from allowing smaller colloids to escape orientational confinement, which could occur if only 2 planes are used to steer motion.