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Earthworms often form a cluster, from which they can barely free themselves. A similarly active, writhing structure forms when the tentacles of lion's mane jellyfish become entangled. Robotic grippers utilize this principle by using multiple synthetic flexible arms to grip and move objects. And such interlinked self-propelled filaments can also be found at the smaller micrometer scale, for example in a biological cell.

The chains or tentacles are also known as polymer chains. Where they are only subject to thermal noise, the structure and dynamics of such tangles are described by conventional polymer physics. The theoretical description is based on a tube model: A polymer chain moves randomly back and forth within a convoluted tube formed by its neighbors.

Professor Dr. Hartmut Löwen from the Institute for Theoretical Â鶹ÒùÔºics II at HHU says, "Using this model, physicists can predict how quickly a chain can extricate itself from a cluster. The time needed is determined via a so-called scaling law with a universal exponent and is closely correlated to the length of the chain, i.e. how much longer does it take until a chain has freed itself when it is twice as long." Pierre-Gilles de Gennes was awarded the Nobel Prize in Â鶹ÒùÔºics in 1991 for this polymer modeling.

However, it was not known how the model changes when the polymers are active. For example, when they are made up of randomly writhing chains of living worms. This central question from the research field of "active soft matter" has long remained unanswered.

Researchers from HHU, the Technical University of Darmstadt and Dresden University of Technology have, in collaboration with the Max Planck Institute for the Â鶹ÒùÔºics of Complex Systems in Dresden, now uncovered these dynamics with the help of large-scale computer simulations. in Nature Communications , they were able to show that the scaling laws change fundamentally: the associated exponent changes significantly compared with the passive case of randomly externally initiated chains.

In the process, the researchers not only determined the new exponent, but also created a new tube model in which the new phenomena can be classified and clearly understood. With the model, they established that the rigidity of this living polymer mass increases significantly as internal grip forces cause a living system to entangle and block itself.

Lead author Dr. Davide Breoni, who gained his doctorate under the supervision of Professor Löwen and now conducts research in Trento, Italy says, "Preparing these clusters for various polymer sizes in our computer model was painstaking work. However, we were then able to numerically extract the underlying scaling laws for various polymer lengths."

Dr. Suvendu Mandel, who worked as a postdoc at HHU and now works in Darmstadt, continues, "The new laws revolutionize polymer physics. They show that it is very easy for living systems to become collectively entangled, increasing their rigidity overall. Intuitively, one would expect the opposite—that their active movement enables them to untangle themselves more quickly."

Professor Löwen indicates a practical benefit of these findings: "They could enable the development of new 'smart materials,' which become more rigid at the push of a button, i.e. which can drastically alter their viscoelastic properties."