Skip to main content

MINI REVIEW article

Front. Phys.
Sec. Complex Physical Systems
Volume 12 - 2024 | doi: 10.3389/fphy.2024.1358766
This article is part of the Research Topic Static and Dynamic Pattern Formation from Nano to Macro scales View all 8 articles

Theory of Turing pattern formation and its experimental realization in the CIMA reaction system in the presence of materials lowering the diffusivity of activators

Provisionally accepted
  • Faculty of Science and Technology, Keio University, Yokohama, Kanagawa, Japan

The final, formatted version of the article will be published soon.

    In 1952, Alan Turing accomplished a pioneering theoretical study to show that the coupling of nonlinear chemical reactions and diffusion leads to the instability of spatially homogeneous states. The activator and inhibitor are synthesized as intermediates of the reaction system in the Turing model. Turing found that spatially periodic stationary concentration patterns are spontaneously generated when the diffusion coefficient of the activator is lower than that of the inhibitor. The first experimental realization of Turing pattern was achieved in 1990 in a chlorite-iodide-malonic acid (CIMA) reaction system. Iodide and chlorite anions act as the activator and inhibitor of this reaction system, respectively. Although there is no significant difference in the diffusion coefficient of iodide and chlorite anions, the Turing pattern was generated, because starch was added into the gel reactor to enhance the color tone. This formed a complex with iodide to inhibit its diffusion to satisfy the condition for the Turing instability. Several examples were found after this finding. We focused on the high affinity of quaternary alkyl ammonium cations to iodide. The CIMA reaction was performed in an open gel reactor by adding a quaternary alkyl ammonium cationic surfactant. In addition, the polymer gel consists of the quaternary alkyl ammonium group as the side chain was utilized for the open gel reactor. The micelles of the surfactants and the polymer gels trapped iodide in their vicinity as a counter anion to lower the effective diffusivity to satisfy the condition for the Turing instability.

    Keywords: Turing pattern formation, Reaction-diffusion system, growth of spatio-temporal fluctuation, activator and inhibitor, CIMA reaction system, materials lowering the diffusivity of activators, quaternary alkyl ammonium group

    Received: 20 Dec 2023; Accepted: 05 Jul 2024.

    Copyright: © 2024 Aizawa and Asakura. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

    * Correspondence: Kouichi Asakura, Faculty of Science and Technology, Keio University, Yokohama, 223-8522, Kanagawa, Japan

    Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.