Targets, ripples and spirals in a precipitation system with anomalous dispersion

Abstract

We present a novel reaction-diffusion system that exhibits three-dimensional superdiffusive traveling waves without utilizing any external forces. These waves include single circular targets, spirals, and ripples as well as phase-like waves. The system is based on the interplay of the precipitation reaction of mercuric iodide in a gel medium, its polymorphic transformation to a different crystalline form, and its redissolution in excess iodide. A phase diagram is constructed as a function of the initial concentrations of the reagents. The spatiotemporal evolution of these waves is thoroughly analyzed and seems to be a consequence of an anomalous dispersion relationship. Pattern selection and wavelengths of propagating waves are found to depend on initial concentrations of the reactants. The breakup of the waves is also investigated. While the breakdown of ripples and spirals is shown to be a consequence of a Doppler-like instability in conjunction with anomalous dispersion, the targets undergo a boundary defect-mediated breakup.

Pattern Formation in Precipitation Reactions: The Liesegang Phenomenon

“…In such a way, a thin and moving precipitation layer evolves in the gel driven by diffusion with decreasing velocity. The spontaneous appearance of traveling waves (spirals and target patterns) inside this thin and moving precipitation front in a hydrogel medium is reported in several precipitation reactions with complex formation: aluminum hydroxide (Al 3+ (aq) + 3OH – (aq) → Al­(OH) 3 (s), Al­(OH) 3 (s) + OH – (aq) → [Al­(OH) 4 ] − (aq)), , mercuric iodide (Hg 2+ (aq) + 2I – (aq) → HgI 2 (s), HgI 2 (s) + 2I – (aq) → [HgI 4 ] 2– (aq)), − and zinc hydroxide (Zn 2+ (aq) + 2OH – (aq) → Zn­(OH) 2 (s), Zn­(OH) 2 (s) + 2OH – (aq) → [Zn­(OH) 4 ] 2– (aq)) precipitation systems (Figure ).…”

“…Contrary to what is normally expected in waves propagating in other reaction−diffusion systems, these precipitation waves display superdiffusive behavior whereby the temporal evolution of the wave position (d) follows the power law d ∝ t α , with values of the exponent α in the range of 0.65−0.84 depending on the initial concentrations of the reactants. 75,76 This superdiffusive behavior is unexpected because in the system the transport of the chemical species is purely diffusive, and no system with Brownian transport should show superdiffusive characteristics. It is known from previous investigations that the layer of the precipitate in which wave propagation occurs is not homogeneous and it has a special hierarchical structure containing different polymorphs of the precipitate.…”

Self-organization in precipitation reactions far from the equilibrium

“…showed that increasing the inner electrolyte concentration (Hg 2+ ) results in the disruption of the circular precipitation fronts and the formation of irregular, sharp cusps ( Fig. 4I ) ( 173 , 174 ). By comparison, increasing the outer electrolyte concentration (I − ) has a direct influence on the reaction dynamics, and the system transitions from superdiffusive to subdiffusive transport.…”

Low-Cost, High-Performance Sample Cell for X-Ray Spectroscopy of Solutions and Gels Made from Plastic Straw

“…The interest in self-organized pattern formation via precipitation reactions coupled with diffusion in gels/solutions has recently resurged, [1][2][3][4][5] partially because of its relevance in micro-and nanotechnology. [6][7][8] The concentration distribution of each element and the chemical states of the locally formed species are indispensable pieces of information for thorough understanding of these pattern formation processes.…”