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

Abstract

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 the 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 to 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.