Emergent microrobotic oscillators via asymmetry-induced order

The study addresses how to realize slow, self-sustaining oscillations at the microscale—crucial for autonomous functions like locomotion and actuation—without relying on bulky electronics or complex chemical oscillators. Biological systems commonly operate below 100 Hz due to energy and process timescale constraints, but producing similarly slow self-oscillations in artificial microsystems is difficult. Prior approaches often require complex chemistries (e.g., Belousov–Zhabotinsky), responsive materials, or large-scale devices, and generating slow periodic electrical signals on untethered microscale devices is particularly challenging due to the scaling limits of capacitors/inductors and the power/footprint of CMOS oscillators and dividers. This work proposes a collective of simple catalytic microparticles at an air–liquid interface that, through far-from-equilibrium self-organization and intentional permutation symmetry breaking, can transduce chemical energy into robust chemomechanical and electrochemical oscillations suitable for powering microrobotic components.

The paper situates its contribution against several strands of prior work: (1) self-oscillations in biology occur at low frequencies to match energy and process timescales; (2) microscale self-sustaining mechanical oscillations have typically relied on complex chemical oscillators or coupling responsive materials to thermal, chemical, or moisture stimuli, mostly at millimetre scales; (3) producing slow periodic electrical signals on untethered microsystems is hindered by the poor downscaling of capacitors/inductors and the power/area demands of CMOS oscillators, dividers, and energy modules; (4) recent progress achieved self-sustaining electrical oscillations by mechanically modulating resistance in designed devices, suggesting sub-500 µm electrical self-oscillators are possible. In catalytic micromotors, buoyancy and capillary interactions (Cheerios effect) and bubble dynamics can drive repetitive motions, and bimetallic nanomotors use fuel-cell-like electrochemistry to generate voltages for propulsion. Asymmetry-induced order in networked systems and Rattling Theory provide theoretical frameworks showing that heterogeneity can stabilize ordered collective behavior. The present work leverages these ideas to produce and stabilize low-frequency microrobotic oscillations via symmetry breaking.

System and particle design: Microparticles comprise a polymeric SU-8 microdisc (10 µm thick) with a nanometre-thick Pt catalytic patch (typical radius 125 µm; DL particles use 175 µm) on the underside. Particles are placed at the curved air–liquid interface of a 1 mL H2O2 drop. The Pt catalyzes 2H2O2 → 2H2O + O2 (bubble formation). For electrical generation, bimetallic patches (Pt with Au or Ru) are patterned to form on-board fuel cell electrodes (Pt oxidation, Ru/Au reduction), with surrounding surfaces passivated. Experimental conditions and imaging: Experiments primarily use 10.7 wt% H2O2 (unless noted) dispensed onto a polystyrene Petri dish. Particles are transferred by wet or dry methods to ensure correct orientation at the interface. Beating behavior is recorded at 30 fps using a macro/micro imaging system with fiber optic illumination. Dynamics and measurements: For a single particle, bubble growth self-limits access to the catalyst, leading to near-equilibrium with a terminal bubble radius and minimal motion. With two identical particles, bubbles merge upon proximity, restoring catalytic area and enabling further growth until rupture; collapse imparts impulses that separate particles, which then return via radial buoyancy and capillary (Cheerios) attractions, producing a repeatable cycle of approach, contact, bubble coalescence, and collapse ("particle beating"). The collective state is characterized by the breathing radius r(t): the average Euclidean distance from the centroid to particles. Periodicity is assessed via time traces, phase portraits (v(t) = [r, ṙ] after filtering), recurrence time histograms, and recurrence entropy (embedding dimension and ε chosen per Methods). Interarrival time distributions of bubble bursts are extracted to quantify periodicity versus aperiodicity. Modeling: A mechanistic model includes buoyancy Fg, capillary attraction Fc, and non-Stokesian drag Fa, capturing r(t) dynamics and frequency dependence on H2O2 concentration via Langmuir–Hinshelwood surface kinetics. Rattling Theory provides a thermodynamic framework linking driven degrees of freedom and system-level fluctuations; an analytical model connects a particle’s relative bubble size (burst intensity) to collective disorder (Rattling R), predicting reduced R (more order) when one particle differs in bubble size. Symmetry breaking experiments: Permutation symmetry is intentionally broken by introducing a designated leader (DL) particle with a larger Pt patch, thereby generating a larger bubble and faster growth rate. The coalescence of unequal bubbles enters a sticking regime: the merged bubble remains under the DL rather than centered between particles, leading to repeated subsumption of neighbor bubbles and eventual collapse of the enlarged DL bubble at a rupture radius ~1.7× that of homogeneous systems, yielding lower-frequency oscillations. Periodicity across system sizes N is compared between homogeneous and DL-heterogeneous ensembles using interarrival distributions, r(t), phase portraits, and recurrence entropy up to N = 11. Electrochemical microgenerators and actuation: Bimetallic fuel cell particles (Pt-Ru or Pt-Au) are characterized in 25.8 wt% H2O2 with 0.075 M KNO3. Open-circuit voltage and short-circuit current density are measured; bubble size modulates inter-electrode conductance, producing oscillatory currents synchronized with mechanical beating. A Pt-Ru device with leads (passivated) is electrically connected to a Pt-Ti bimorph microactuator (fabricated on a Cu sacrificial layer; lifted into PBS). Oscillatory current from two beating particles cyclically drives actuator deswelling/swelling; actuator length change is recorded and compared with current traces. Fabrication (summary): SU-8 discs are photolithographically patterned on Si; Pt patches (5 nm Cr/Ti adhesion, 50 nm Pt) are e-beam evaporated and liftoff performed; particles are released from Si in KOH and rinsed. Fuel cell electrodes on glass are patterned with LOR/Shipley resists; Ti/Pt and Ti/Au or Ru are deposited; SU-8 passivation windows are defined. Microactuators are fabricated per prior methods and released by Cu etch. Detailed spin, bake, exposure, development, and lift-off parameters are provided in Methods.

- Emergent low-frequency chemomechanical oscillations: Two identical particles at the H2O2 air–liquid interface exhibit stable, repeatable beating cycles driven by bubble coalescence and collapse, with a measured period of ~3.2 s in 10.7 wt% H2O2. r(t) trajectories, closed-loop phase portraits, and narrow recurrence peaks confirm periodicity and long-term stability. Fuel consumption over 280 s is negligible (~0.02%). The mechanistic model reproduces r(t) features and predicts frequency tuning with H2O2 concentration, matching experiments. - Scalability and tuning: Oscillations persist for particle diameters down to 250 µm and 100 µm. Beating frequency depends on H2O2 concentration as predicted by Langmuir–Hinshelwood kinetics. - Loss of periodicity with homogeneous ensembles: In systems of identical particles, interarrival time distributions show diminishing periodic peaks and increasing sub-1 s stochastic bursts as N increases; by N ≥ 8, distributions are statistically indistinguishable from a Poisson process. r(t) exhibits low-amplitude, aperiodic fluctuations (e.g., N = 8). - Asymmetry-induced order via designated leader (DL): Rattling Theory predicts reduced disorder R when one particle’s relative burst intensity deviates from 1×, especially for stronger (larger-bubble) particles. Introducing a DL with a larger Pt patch experimentally yields sharp interarrival peaks and robust periodicity across N (up to N = 11). Example: N = 7 + 1DL shows stable long-term oscillations with period ~14.2 s. Recurrence entropy remains low and invariant to N for DL systems, while it increases linearly with N in homogeneous systems. - Bubble coalescence physics: Heterogeneous pairs enter a sticking regime where merged bubbles remain under the DL, enabling successive subsumption of neighbor bubbles. DL bubble rupture radius is ~1.7× that of homogeneous systems, contributing to lower-frequency oscillations (e.g., N = 2 DL system period ~42 s in recurrence analysis). - On-board electrical generation: Bimetallic fuel cell particles generate voltages/currents from the same H2O2 chemistry while bubble dynamics modulate conductance to produce oscillatory currents in phase with mechanical beating. Measured in 25.8 wt% H2O2 with 0.075 M KNO3: Pt–Ru OCV 144.9 ± 2.4 mV; Pt–Au OCV 21.4 ± 3.5 mV. Pt–Ru short-circuit current density 1.71 ± 0.38 mA/cm², current 56.7 ± 12.4 nA. ON/OFF current ratio can exceed 10^6 between no bubble and threshold bubble size. - Microrobotic actuation: The oscillatory current cyclically actuates a Pt–Ti bimorph microactuator in synchrony with beating; actuator length changes track current spikes. A stabilized, heterogeneous configuration yields sub-0.03 Hz beating in this demonstration. - Comparative benchmark: Achieved peak currents are comparable to or exceed those in significantly larger thermo-mechano-electrical oscillators (e.g., −47 nA reported for a 1.5 × 6 cm device).

The findings show that simple catalytic microparticles can self-organize into reliable low-frequency oscillators by exploiting far-from-equilibrium bubble dynamics and environmental forces. While homogeneous collectives lose periodicity as size increases, intentional permutation symmetry breaking—implemented via a designated leader with enhanced catalytic area—induces asymmetry-driven order that stabilizes periodic beating across ensemble sizes. Rattling Theory provides a thermodynamic explanation: heterogeneity adjusts system-level fluctuations, lowering Rattling and promoting correlated, ordered dynamics. This mechanistic understanding directly addresses the challenge of generating slow, self-sustaining oscillations at the microscale without complex electronics or chemistries. Critically, the same chemical process simultaneously drives mechanics, generates voltage, and modulates conductance, enabling on-board oscillatory electrical currents sufficient to power state-of-the-art microactuators. This demonstrates a pathway toward autonomous microrobotic systems that leverage embodied energy and environmental coupling to reduce design complexity. The robustness to particle count in heterogeneous systems and the tunability of frequency via fuel concentration expand the operational design space for active matter-based micromachines.

The work introduces a microrobotic oscillator that emerges from the collective behavior of catalytic microparticles at an H2O2 air–liquid interface. By breaking permutation symmetry with a designated leader particle, the system exhibits asymmetry-induced order, maintaining robust low-frequency periodic beating across ensemble sizes where homogeneous systems fail. A mechanistic model and Rattling Theory explain how heterogeneity reduces disorder and stabilizes limit cycles. The collective’s self-oscillations are harnessed via a simple bimetallic fuel cell to produce oscillatory electrical currents capable of cyclically driving a Pt–Ti microactuator, eliminating the need for external power sources or complex electronics. These contributions provide a general strategy for microscale low-frequency oscillators and lay groundwork for autonomous microrobots that exploit environmental physics. Future work includes scaling to larger collectives, exploring topology and symmetry effects on active matter organization, and integrating sensors and computation to enable complex inter-particle communication and task execution.

- Demonstrated robustness to particle number is established up to N = 11; behavior at larger N is left for future study. - Operation relies on an H2O2 droplet air–liquid interface and specific capillary/buoyancy conditions; generalization to other fuels, interfaces, or fully submerged/solid-state environments is untested. - Electrical performance metrics (OCV, current density) are characterized in relatively high H2O2 concentration (25.8 wt%) with added electrolyte; performance in lower concentrations or different electrolytes may vary. - Frequency and stability depend on particle sizes, geometry (e.g., DL patch radius), and fuel concentration; detailed long-term durability and degradation of catalytic surfaces and actuators are not reported. - Control over precise timing/phase in larger heterogeneous networks and integration with complex loads/sensing remain to be developed.