Exploring chaos on the nanometer scale

Apex of an ellipsoidal Rh nanocrystal. a Schematics of the experimental setup and the sample geometry: in FEM and FIM, field emitted electrons and ions, respectively, form a point projection image of the sample surface. The apex of the [110]-oriented Rh nanocrystal has axis lengths of a, a′, b and c. b FIM image of the Rh nanocrystal, obtained at T = 77 K using Ne+ ions. c the same field of view, but in the FEM mode, with the same crystallographic markings as in b. d Ball model of the nanocrystal apex with crystallographic net overlay, where each of the four triangles forming the net corresponds to the inverse pole figure (bottom right). To illustrate the local atomic corrugation, the individual atoms are color-coded according to their nearest and next-nearest neighbor numbers. Credit: Nature Communications (2023). DOI: 10.1038/s41467-023-36434-y

Chaos theory has been a topic of research for decades, and its application in chemical reactions on larger or macroscopic systems has been successful. However, chaotic behavior has not been detected on the nanometer scale, where other effects are expected to predominate. This introduction provides an overview of the study conducted by scientists from TU Wien, who were able to detect indications of chaos on the nanometer scale in chemical reactions on tiny rhodium crystals. The researchers discovered that the crystal consists of many different surface nanofacets, each of which exhibits oscillating behavior, and their behavior is coupled with that of neighboring facets. The study's findings have significant implications for understanding chemical reactions and biological systems.

The Simple Chemical Reaction and Its Oscillating Behavior

The chemical reaction studied involves the reaction of oxygen with hydrogen, facilitated by a precious metal catalyst, to produce water, which is the basic principle of a fuel cell. The reaction rate is affected by external conditions, such as pressure and temperature. However, under specific conditions, the reaction shows oscillating behavior, despite the constant external conditions. The catalytic system oscillates between inactive and active states, as the reaction rate oscillates between barely perceptible and high. This oscillation is similar to the back-and-forth movement of a pendulum, and the researchers observed this behavior in chemical reactions on a rhodium nanocrystal.

The Predictability of Pendulums and the Butterfly Effect

A pendulum is a classic example of a predictable system. If a pendulum is disturbed or set in motion twice in slightly different ways, it behaves broadly the same. This predictability is the opposite of chaotic systems, where minimal differences in the initial conditions lead to strongly differing results in long-term behavior. Several pendulums connected by elastic bands are an example of this behavior. While the laws of nature determine how pendulums behave, it is impossible to recreate the same initial situation twice in practice. Even a vanishingly small difference in the initial conditions leads to a completely different system behavior. This is known as the butterfly effect.

The Emergence of Chaos on the Nanometer Scale

The study conducted by TU Wien researchers found clear indications of chaos on the nanometer scale in chemical reactions on tiny rhodium crystals. Each facet of the crystal exhibits oscillating behavior, but their reactions are coupled with those of neighboring facets. The coupling behavior is controlled by changing the amount of hydrogen. Initially, one facet dominates and sets the pace, and all other facets oscillate to the same beat. If the hydrogen concentration increases, different facets oscillate at different frequencies, but their behavior is still periodic and predictable. However, if the hydrogen concentration is further increased, the order breaks down, and chaos prevails. The oscillations become unpredictable, and small differences in the initial situation lead to completely different oscillation patterns.

The Role of Stochastic Noise and the Theoretical Model

The researchers noted that the smaller the system, the greater the contribution of stochastic noise. This noise, which is distinct from chaos, is expected to dominate the behavior of the system. Therefore, it was surprising to observe indications of chaos on the nanometer scale. The researchers used a theoretical model developed by Prof. Keita Tokuda, which was particularly useful in explaining the observed chaotic behavior.

The Implications for Nano-Chemistry and Biological Systems

The findings of this study have significant implications for understanding chemical reactions and biological systems. Small deviations in the symmetry of the crystal can determine whether the catalyst behaves in an ordered and predictable way or in a disordered and chaotic way. This knowledge is essential for different chemical reactions and potentially for biological systems.

This study is the first attempt to transfer the extensive knowledge of chaos theory to the nanometer scale and explore chaotic behavior in chemical reactions on a nanoscale level. The findings of this research are significant, as chaos is typically associated with large-scale systems such as weather patterns, celestial bodies, and coupled pendulums. The discovery of chaos on the nanometer scale has important implications for understanding the behavior of small-scale systems, including catalytic reactions on tiny rhodium crystals.

The research conducted by scientists at TU Wien sheds light on the oscillating behavior of a chemical reaction between oxygen and hydrogen to form water, which is the basic principle of a fuel cell. The reaction rate depends on external conditions such as pressure and temperature, but under certain conditions, the reaction exhibits oscillating behavior despite constant external conditions. The catalytic system oscillates back and forth between inactive and active states, much like a swinging pendulum.

While a pendulum's behavior is predictable, chaos theory demonstrates that minimal differences in initial conditions lead to vastly different results in long-term behavior, as evidenced by several pendulums connected by elastic bands. The same principle applies to the chemical oscillations on a rhodium nanocrystal, where each surface nanofacet exhibits oscillations that are coupled with neighboring facets. Increasing the hydrogen concentration leads to a breakdown of order and the emergence of chaos, where small differences in the initial situation result in vastly different oscillation patterns.

The discovery of chaos on the nanometer scale challenges previous assumptions that stochastic noise dominates the behavior of small-scale systems. The researchers were able to 'extract' indications of chaos through a theoretical model developed by Prof. Keita Tokuda, despite noise's expected contribution to the system's behavior. This research has significant implications for understanding the behavior of small-scale systems, including catalytic reactions, and could provide insight into biological systems.

Journal Information: Maximilian Raab et al, Emergence of chaos in a compartmentalized catalytic reaction nanosystem, Nature Communications (2023). DOI: 10.1038/s41467-023-36434-y