Study shows why 2D materials melt when it gets cold

When it gets warmer, materials melt: for example, the ice on a stick in summer or the snow on the meadow at the first rays of sunshine in spring. In these processes, atoms and molecules move in a disordered way. They no longer stay in one place. A team of researchers from the universities of Kaiserslautern, Bielefeld and Mainz has now shown in a study that this also works in reverse: Molybdenum acetate molecules, which form an ordered structure on the surface of copper at room temperature, are mobilised by cooling, not by heating. The study has been published in the renowned journal Angewandte Chemie.

It seems paradoxical that molecules and atoms start moving by cooling. "Actually, this happens by heating," says Professor Dr Martin Aeschlimann, who heads the Department of Ultrafast Phenomena on Surfaces at the Technical University of Kaiserslautern (TUK). However, the Göttingen chemist Gustav Tammann already speculated about this effect in 1903 and called it "inverse melting". "This phenomenon can be observed in special situations, for example at high pressure or with special materials such as helium," the professor continues. Other materials, for example metal alloys, can indeed change from an ordered to a disordered state through cooling - as in melting - but the particles do not become mobile.

"In our study, we show that molecules have not only become disordered but actually mobile through cooling," says Aeschlimann.

For their work, the research team relied on the compound molybdenum acetate. At room temperature, these molecules form an ordered structure. They are deposited in a single-layer coating on a copper surface. Other working groups have already investigated such two-dimensional systems. However, they have not succeeded in proving that the molecules can be mobilised. Together with researchers from Johannes Gutenberg University Mainz and Bielefeld University led by first author Simon Aeschlimann and Professor Dr Angelika Kühnle, the TUK team has now succeeded for the first time. "We called the process mobilisation by cooling because, strictly speaking, only three-dimensional materials can melt," Professor Aeschlimann continues.

For its study, the team cooled a molecular system of copper and molybdenum acetate to about minus 50 degrees Celsius. They observed that the ordered structure dissolves and the molybdenum acetate molecules become mobile. At room temperature, on the other hand, the molybdenum acetate molecules stand upright and line up in chains. At minus 50 degrees Celsius, this chain structure disintegrates in some areas: Molecules detach themselves from the ends of the chains and reattach themselves elsewhere, or form only single curved chains.

The prerequisite for this effect is a reduction in entropy. "By entropy we mean a measure of the arrangement and movement possibilities that atoms or molecules have in a system," explains Aeschlimann. As a rule, entropy increases when an ordered structure dissolves because the individual particles have more possibilities: For example, they can move in different directions instead of occupying a fixed place. This happens when melting, for example in metals: The ordered structure dissolves, the metal atoms move back and forth and the entropy of the system increases.

The case is different with the molybdenum acetate-copper system: Here, there is only the possibility of moving in the different spatial directions. The molybdenum acetate molecules are arranged in a chain structure. They cannot leave their place. However, they stand upright and are not so strongly bound to the copper surface, so they can move certain parts of themselves. "It's like they're wiggling their ears," Aeschlimann cites as a comparison. In the disordered phase, on the other hand, the molybdenum acetate molecules lie flat on the surface and are more strongly bound. In this case, the molecules can, to stay with the image, crawl back and forth lying on their bellies, but no longer wiggle their ears. Therefore, the entropy of the system decreases, although it changes into a mobile phase.

A scanning tunnelling microscope was used for the study. This involves moving a tiny needle over the materials and measuring the current between the tip of the needle and the surface. This then produces an image of the surface structure. The images show that at lower temperatures, disordered, flaky areas develop instead of a continuous chain structure. The researchers have supplemented this investigation with computer simulations.

The results of the study help to better understand two-dimensional systems and inverse melting processes. Such phase transitions are also interesting for our everyday life, for example, when we want to cool drinks with ice cubes or insulate houses with latent heat storage.

The work took place within the framework of the Collaborative Research Centre (SFB/TRR 88) "Cooperative Effects in Homo- and Heterometallic Complexes (3MET)".

The study was published in the renowned journal "Angewandte Chemie: Mobilization upon Cooling." Simon Aeschlimann, Lu Lyu, Sebastian Becker, Sina Mousavion, Thomas Speck, Hans-Joachim Elmers, Benjamin Stadtmüller, Martin Aeschlimann, Ralf Bechstein, Angelika Kühnle

DOI: doi.org/10.1002/ange.202105100

Questions answered:

Professor Dr Martin Aeschlimann
Department of Ultrafast Phenomena on Surfaces

TU Kaiserslautern
E-mail: ma@physik.uni-kl.de
Tel.: 0631 205-2322