Attractive interactions between particles do not necessarily lead to these particles aggregating. This is the new finding from researchers at the Tokyo University of Science in Japan who say this behaviour comes from non-reciprocal interactions amongst particles of different sizes that exert unequal forces on each other. These interactions could serve as a general design principle for creating active matter with a structure that continuously reorganizes rather than simply relaxing towards a static state.
Nature abounds with examples of active matter, with some well-known examples being flocks of birds, fish and insects, sheets of biological cells and swarms of bacteria. Researchers have been trying to copy this collective behaviour and make synthetic active materials – such as self-propelled colloids and dense phases of mechanically driven biopolymers – in the laboratory. Before such applications see the light of day, however, they need to first understand the fundamental physics of these systems.
In their new study, a team led by Yutaka Sumino and Kiwamu Yoshii of Tokyo University of Science’s department of applied physics, came across a system in which colloidal particles interact through electrohydrodynamic flow. “We found that mixing particles of two different sizes in such a system completely changed the collective behaviour of these particles,” explains Sumino. “Instead of forming increasingly large crystal-like aggregates, as is the case for particles with the same size, the system remained highly dynamic.”
The physicists’ experiment involved suspending polystyrene colloidal particles with radii of 1 and 1.5 µm in water and confining them between transparent indium tin oxide-coated electrodes. This set up allowed them track more than 10,000 particles and quantitatively analyse their dynamics for more than an hour, as opposed to just a few minutes in previous such studies.
Newton’s third law holds
When the researchers applied an alternating electric field to the system, they observed electrohydrodynamic flows around the particles, the strength of which increased strongly as the size of the particles became bigger. The electrohydrodynamic-mediated attractive interactions therefore became asymmetric, they explain, something that causes larger particles to attract smaller ones more strongly. This imbalance leads to non-reciprocal interactions, meaning that a larger particle pushes a smaller one, but a smaller one doesn’t push back.
While the effective interaction between the particles appears to break Newton’s third law, it doesn’t because there is no violation of momentum conservation, explains Sumino: momentum is transferred to the surrounding fluid through the induced flows and is ultimately dissipated through friction with the substrate.
The researchers also observed that particles of different sizes spontaneously pair together to form asymmetric structures with a distinct front and tail. These pairs behave as self-propelled units and move through the suspension – even though individual particles cannot propel themselves. As more self-propelled pairs form, they assemble into larger clusters, but these clusters do not continue growing into large aggregates and instead repeatedly fragment, rearrange themselves and reform. Importantly, they note: “the larger particle tends to be at the front of these moving pairs. This head-heavy size asymmetry, together with excluded-volume interactions, promotes the fragmentation of larger clusters and thereby prevents continuous coarsening”.
Sumino and Yoshii combined their experiments with numerical simulations, thereby identifying non-reciprocal pair motion as the microscopic origin of this behaviour.
The results, they say, suggest that non-reciprocal interactions can serve as a general design principle for creating active materials with structures that continuously reorganize rather than simply relaxing toward a static state. “An interesting aspect,” explains Sumino, “is that self-propulsion does not need to be built into each individual particle: it can emerge collectively from non-reciprocal interactions between particles that do not self-propel on their own.”
Nanoparticles levitated by light exhibit non-reciprocal interactions
If such interactions can be controlled externally, they could provide a way to design microscopic systems that collectively gather, transport, fragment or mix materials, he tells Physics World. “Possible directions include programmable active materials and microrobotic systems, although these applications are still some way off.”
Reporting their findings in Physical Review Letters, the researchers say they would now like to understand how general this non-reciprocal mechanism is and whether the same principle – collective activity emerging from non-reciprocal interactions – can be transferred to other experimental systems. In the system studied in this work, the strength of the non-reciprocity depends on parameters such as particle size, composition and the applied electric field. By systematically tuning these parameters, they aim to explore what other types of collective states can be generated and whether transitions between them can be controlled.
“A more detailed hydrodynamic analysis of the system is also needed to develop a quantitative understanding of the interactions and ultimately predict the collective motion of the colloids,” says Sumino.
