🔬 condensed matter

Multistable energy landscapes for adaptive microscopic machines

This paper demonstrates that designing multistable energy landscapes allows synthetic microscopic machines to autonomously select between multiple functions and dynamic responses under a single external driving field, thereby significantly enhancing their adaptability and autonomy.

Original authors: Melody Xuan Lim, Zexi Liang, Gabriel Alkuino, Jason Z. Kim, Itay Griniasty, Teng Zhang, Paul L. McEuen, Itai Cohen

Published 2026-05-06

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CC BY 4.0

Original authors: Melody Xuan Lim, Zexi Liang, Gabriel Alkuino, Jason Z. Kim, Itay Griniasty, Teng Zhang, Paul L. McEuen, Itai Cohen

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a tiny, microscopic robot. Usually, to make this robot move or change shape, you have to constantly change the signal you send to it. If you want it to open, you send Signal A. If you want it to close, you send Signal B. The robot is like a puppet; its movements are entirely dictated by the puppeteer's hand.

This paper introduces a new way to build these tiny robots so they can be a bit more independent. Instead of just reacting to the signal, the robot is built with an internal "memory" and a set of hidden rules that let it decide what to do based on its own history, even when the signal from the outside stays exactly the same.

Here is how they did it, using simple analogies:

1. The Energy Landscape: A Hilly Playground

Think of the robot's possible shapes as a hilly playground.

The Valleys: The low points in the hills are "stable states." If the robot is in a valley, it likes to stay there.
The Hills: The high points are unstable. The robot naturally wants to roll down into a valley.
The Magic: The researchers designed these "hills and valleys" (which they call an energy landscape) so that the robot has multiple valleys it can sit in.

Usually, if you push a ball down a hill, it goes to the bottom. But here, they built the hill so that depending on where the ball started, it could end up in two different valleys even if you pushed it with the exact same force.

2. Example One: The Memory Switch (Bistability)

Imagine a tiny door that can be either Open or Closed.

Old Way: You need a specific magnet to open it and a different magnet to close it.
New Way: The door is built so that it can stay Closed even if you turn off the magnet, if you pushed it closed first. But if you pull it open and then turn off the magnet, it stays Open.

The robot "remembers" whether it was last pushed open or closed. The external magnetic field is the same in both cases, but the robot's internal state (its history) decides which shape it takes. It's like a light switch that stays in the "on" position even after you stop pushing the button, until you push it again from the other side.

3. Example Two: The Twisting Twist (Two Degrees of Freedom)

Now, imagine that same door, but it can also twist like a corkscrew.

The researchers added a second way for the robot to move: it can bend and twist.
They found that if the robot is in the "Closed" position, a magnetic push makes it just open up.
But if the robot is in the "Twisted-Closed" position, that same magnetic push makes it do something totally different: it untwists and then opens.

It's like having a car with two gears. If you are in "Drive," stepping on the gas moves you forward. If you are in "Reverse," stepping on the gas moves you backward. The "gas pedal" (the magnetic field) is the same, but the car's internal gear (its state) determines the result.

4. Example Three: The Self-Propelled Walker (Locomotion)

Finally, they built a tiny "walker" made of three panels connected by flexible hinges.

This walker is symmetrical, meaning it looks the same from all sides.
When they wiggle the magnetic field up and down, the walker doesn't just wiggle in place. Because of its internal design and the way it moves, it takes a step forward.
The Cool Part: The walker decides which way to go based on how it was last positioned. If it's facing North, it walks North. If it's facing South, it walks South. The magnetic field doesn't tell it "Go North"; the field just provides the energy, and the walker's own shape and history tell it where to go.

Why This Matters (According to the Paper)

The paper claims this is a big step toward autonomy.

Current Robots: Need a complex, constantly changing signal to do complex things.
These Robots: Can take a simple, repetitive signal (like a steady magnetic wiggle) and turn it into complex, adaptive behavior (walking, switching states, or moving fluid) because the "intelligence" is built into the physical shape and the energy landscape of the machine itself.

The authors also note that while they used magnetic fields for this, the same idea could work with light, sound, or mechanical forces. The key is designing the "hills and valleys" so the machine can store information about its past and react differently to the same present moment.

Technical Summary: Multistable Energy Landscapes for Adaptive Microscopic Machines

Problem Statement
Recent advancements have enabled the fabrication of synthetic microscopic machines powered by external fields (light, acoustic, or magnetic). However, a fundamental limitation persists: the function of these machines is typically controlled directly by the externally applied field, which deterministically specifies instantaneous dynamics. This global control prevents differential functionality based on the device's internal state or environmental history. Consequently, machines cannot adaptively respond to changes in their environment or store information about past stimuli to dictate future actions. The challenge is to design microscopic machines that can encode internal states and execute multiple distinct functions under the same external driving field, thereby increasing autonomy.

Methodology
The authors propose a strategy based on programmable multistable energy landscapes. Inspired by biological proteins that encode internal states in their conformation, the team designs synthetic magneto-elastic microscopic machines where the internal structure dictates the response to an external magnetic field.

Fabrication: The devices are fabricated using a multi-layer lithography process on silicon substrates. They consist of rigid panels patterned with nanomagnets (cobalt) connected by flexible polymer hinges (DUV42P anti-reflective coating). The magnetic dipole moments are controlled via electron-beam lithography, while the elastic properties are defined by the hinge geometry (width and thickness).
Energy Landscape Design: The total energy of the system ( $U_{tot}$ ) is the sum of elastic energy, magnetic dipole-dipole interaction energy, and the interaction energy with the external magnetic field. By tuning the number of magnets, their orientation, and the hinge dimensions, the authors engineer potential energy landscapes with multiple minima (stable states).
Actuation: The devices are actuated by uniform magnetic fields generated by Helmholtz coils. The response is visualized via optical microscopy and validated through molecular dynamics simulations and analytical bifurcation theory.

Key Contributions and Results
The paper demonstrates three distinct levels of autonomy, progressing from simple bistability to complex locomotion:

Bistable Memory (Two-State Device):
- Design: A two-panel device connected by an elastic hinge.
- Result: The device exhibits two stable mechanical configurations ("open" and "closed") under the same range of external magnetic fields. The state the device occupies depends on its history of actuation rather than the instantaneous field value.
- Mechanism: Below a critical threshold field ( $B^*$ ), the closed state remains stable due to magnetic dipole-dipole interactions overcoming the elastic restoring force. Above $B^*$ , the closed state destabilizes, and the device re-opens. This decouples the device configuration from the instantaneous field, allowing the device to "remember" past forces. The threshold $B^*$ is predictable via bifurcation theory based on hinge width and magnet count.
Orthogonal Dynamic Responses (Two Degrees of Freedom):
- Design: An expansion of the two-panel device to include a twisting degree of freedom ( $\phi$ ) in addition to the bending angle ( $\theta$ ). This creates a "twist-closed" state.
- Result: The same external magnetic field perturbation induces different conformational changes depending on the initial state.
  - From the standard "closed" state, an out-of-plane field causes the panel to lift and align with the field.
  - From the "twist-closed" state, the same field causes the panel to lift and spontaneously untwist the hinge.
- Application: By cycling between these states (open $\to$ twist-closed $\to$ untwisting $\to$ open), the device traces a non-reciprocal cycle in configuration space. This encloses an area in the energy landscape, generating a net displacement of the surrounding fluid environment.
Autonomous Locomotion and Interaction (Symmetric Device):
- Design: A three-panel "walker" with a magnetic "head" and two non-magnetic "tail" panels, symmetric with respect to rotation about the vertical axis.
- Result: A single degree-of-freedom magnetic input (oscillating in-plane and out-of-plane) drives autonomous locomotion. Because the device is rotationally symmetric, the direction of motion is determined by the device's initial orientation (its internal state history), not the direction of the global magnetic field.
- Adaptivity: The walkers can navigate in any direction with equal efficiency. Furthermore, they demonstrate adaptive behavior by altering their heading in response to steric contact or hydrodynamic forces exerted by other walkers, effectively "metabolizing" a neutral energy input to perform work and interact with peers.

Significance
The paper claims that designing multistable energy landscapes is a crucial step toward realizing adaptive microscopic machines. By shifting the control paradigm from global field specification to local energy landscape engineering, the authors demonstrate that:

Microscopic machines can store information about past stimuli in their internal conformational state.
The same external driving field can be used to execute multiple, distinct functions (no response, switching states, or net displacement) based on the device's history.
This approach allows for the construction of machines that autonomously navigate and interact with their environment without requiring complex, real-time external feedback loops.

The authors frame this work as a minimal model system for testing theoretical design principles for microscale robotics, suggesting that the ability to precisely design energy landscapes and their gradients is a foundational step toward autonomous microrobotics. They note that while magnetic forces were used here, the principles extend to any external force capable of altering device configuration, including mechanical, optical, or fluidic signals.