Spiral patterns and morphology in chemical systems
Oliver Steinbock
Florida State University,
Department of Chemistry and Biochemistry,
Tallahassee, FL 32306-4390, USA
E-mail: osteinbock@fsu.edu
Synopsis
This talk will showcase different examples of chemical systems undergoing self-organization far
from the thermodynamic equilibrium. Starting with a brief look at the history of chemical waves
and the work of the field’s pioneers, we will discuss similarities to the growth of unusual
polycrystalline solids called biomorphs and go beyond to the self-propulsion of chemical gardentubes.
Abstract
Living systems masterfully program molecular events to create macroscopic shapes anddynamics. Can the same be done with inorganic chemistry? I believe the answer is yes if
reactions are kept far from the thermodynamic equilibrium (and your expectations are not toohigh). In my talk, I will introduce several self-organizing chemical systems including theBelousov-Zhabotinsky (BZ) reaction, chemical gardens, biomorphs, and self-propelled catalytic
units capable of swarm-like cooperativity. These examples will illustrate unexpected behaviors
if reactions are allowed to unfold in space and time. Perhaps not surprisingly, similar processes
are used by living systems suggesting system-level interpretations of important biologicalphenomena (e.g. cardiac arrhythmia) and novel approaches to materials science andengineering.
Our discussion of the BZ reaction will focus on three-dimensional patterns and discuss them inthe context of pioneering work by Profs. Stefan Müller, Benno Hess, and Art Winfree. These andother prominent scientists studied two-dimensional spirals, the basic building blocks of scroll
waves that provide the foundation for understanding 3D dynamics. While spiral waves rotate
around point singularities, scroll waves rotate around 1D filaments that move according to theirlocal curvature. Today tomographic methods, numerical simulations, and controlled
manipulations are used to obtain deeper insights into the local pinning to heterogeneities aswell as scroll behavior in gradients. Many of these studies, including the results to bepresented, are motivated by similar phenomena in the ventricles of the human heart and theirlink to sudden cardiac death.

Similar nonlinear wave dynamics appear to rule the growth of certain polycrystalline assemblies
known as biomorphs. The smoothly curved and life-like biomorphs form when aqueous
solutions of BaCl2 and silicate react with CO2. The shapes are about 100 μm in size and include
helices, funnels, and urns. The entirely abiotic biomorphs can form from natural spring waters
and constitute intriguing problems for the identification of Earth’s earliest microfossils as wellas the search for life’s remnants on Mars and other planetary bodies.
Lastly, we will present novel results on chemical gardens (CG). In the classical CG experiment,these colorful, hollow precipitate tubes form when a salt crystal is placed into an alkaline
sodium silicate solution. Specific aspects to be covered include a cellular automaton model ofCGs, the involvement of colloidal particles in their growth, and applications as self-propelled
micro-rockets. Our model considers, CG growth based on a simple A+B->C reaction and a lattice
for which each site is exactly one of these three species. We show that the aging of the material
modulates the likelihood of mechanical changes in the position of the solid product C and that astrong preference for changes in the fresh material causes filament (2D) and tube (3D) growth.
The self-propulsion of CG tubes is demonstrated for Mn-containing units in H2O2 solutions. Thetubes are propelled forward by the rhythmic ejection of O2 microbubbles formed in thecatalytic tube cavity. We also observed a characteristic acoustic signature of this propulsionthat allows detailed analyses of the bubble dynamics. These analyses reveal that the tube speed
is determined by the tube diameter (which approximates the step size per bubble) and thebubble ejection frequency (which is nearly proportional to the H2O2 concentration). Lastly, wewill discuss the swarming behavior of the CG tubes and their interactions with bubble rafts.

References[1]
F. M. Zanotto and O. Steinbock, “Hyperscroll Dynamics: Vortices in Four-dimensionalNetworks”, Chaos 31, 053132, 2021.
[2]
P. Knoll, N. Wu, and O. Steinbock, “Spiraling Crystallization Creates Layered Biomorphs”,
Phys. Rev. Materials 4, 063402, 2020.
[3]
B. C. Batista, A. Z. Morris, O. Steinbock, “Pattern selection by material aging: Modelingchemical gardens in two and three dimensions”, Proc. Natl. Acad. Sci. USA 120, e2305172120
2023.