A Theoretical Study on Turing Patterns in Electrochemical Systems

We present theoretical studies on pattern formation in electrochemical systems with an S-shaped current potential curve (S−NDR systems) under potentiostatic control. Linear stability analysis and simulations of the reaction−migration equation give evidence that stationary patterns with a defined wavelength exist in a large parameter range. As it is the case for Turing structures, the patterns form due to an interplay of short-range activation and long-range inhibition. It is shown that the constraint on the ratio of the diffusion constants of activator and inhibitor in reaction−diffusion equations transforms into a condition involving diffusion and migration lengths of the system. This condition is fulfilled in practically all electrochemical systems. The experimental parameters under which the patterns form should be readily accessible.