Bifurcation analysis of bistability between spatially uniform and non-uniform electrochemical oscillations

Production of Noble-Metal Nanohelices Based on Nonlinear Dynamics in Electrodeposition of Binary Copper Alloys

Spatiotemporal pattern formation is dynamic self-organization widely observed in nature and drives various functions. Among these functions, chirality plays a central role. The relationship between dynamic self-organization and chirality has been an open question; therefore, the production of chiral nanomaterials by dynamic self-organization has not been achieved. Here, we show that the confinement of a two-dimensional spatiotemporal micropattern via the electrodeposition of a binary Cu alloy into a nanopore induces mirror symmetry breaking to produce a helical nanostructure of the noble-metal component although it is still not yet possible to control the handedness at this stage. This result suggests that spatiotemporal symmetry breaking functions as a mirror symmetry breaking if cylindrical pores are given as the boundary condition. This study can be a model system of how spatiotemporal symmetry breaking plays a role in mirror symmetry breaking, and it proposes a new approach to producing helical nanomaterials through dynamic self-organization.

Spontaneous Symmetry Breaking of Nanoscale Spatiotemporal Pattern as the Origin of Helical Nanopore Etching in Silicon

Nanometric chiral objects such as twisted or helical nanoribbons represent a new class of objects having important potential in a large panel of applications, taking advantage, for example, of electromechanical or optical chirality, local chiral environment for catalysis, and chiral recognition. Supramolecular chemistry has played a central role in the production of such structures through either chiral macromolecules/foldamers or the self-assembly of chiral molecules; the latter can also be used as templates for the sol-gel transcription to silica materials, offering them polymorphisms with further structural stability. Here, we report a totally different and dynamic approach to produce helical mesostructures. This study focuses on helical nanopores that are spontaneously formed in the platinum-assisted chemical etching of silicon by dynamic self-organization under a nonequilibrium state. The symmetry breaking of a helical nanopore formation is achieved by the spatial symmetry breaking of a spatiotemporal pattern at the nanoscale and without incorporation of chiral molecules. Rotational motion of the platinum nanocatalyst, which is regarded as a spatiotemporal pattern at the etching frontier (the platinum/silicon interface), induces precession movement of the nanocatalyst, and movement of the catalyst during etching forms helical nanopores in the silicon. We consider that this study is an important milestone to understand the close relation between spatiotemporal pattern formation and the dynamic emergence of symmetry breaking in chemical reactions.

Normal-form approach to spatiotemporal pattern formation in globally coupled electrochemical systems

We show that the experimental global coupling (GC) of spatially extended electrochemical oscillators is weak close to a supercritical Hopf bifurcation. A center manifold reduction allows then the normal form which comprises the GC and the naturally existing nonlocal (migration) coupling (NLC) to be derived. We show that the interaction between NLC and GC widens the spectrum of coherent structures found in globally coupled oscillatory media and allows for wavelength selection of standing waves, stabilization of phase clusters without breaking phase invariance, and creation of heteroclinic networks connecting families of oscillatory states characterized by different spatial symmetries.