Superdiffusive Cusp-Like Waves in the Mercuric Iodide Precipitate System and Their Transition to Regular Reaction Bands

We
report a two-dimensional (2D) reaction–diffusion system
that exhibits a superdiffusive propagating wave with anomalous cusp-like
contours. This wave results from a leading precipitation reaction
(wavefront) and a trailing redissolution (waveback) between initially
separated mercuric chloride and potassium iodide to produce mercuric
iodide precipitate (HgI2) in a thin sheet of a solid hydrogel
(agar) medium. The propagation dynamics is accompanied by continuous
polymorphic transformations between the metastable yellow crystals
and the stable red crystals of HgI2. We study the dynamics
of wavefront and waveback propagation that reveals interesting anomalous
superdiffusive behavior without the influence of external enhancement.
We find that a transition from superdiffusive to subdiffusive dynamics
occurs as a function of outer iodide concentration. Inner mercuric
concentrations lead to the transition from the anomalous cusp-like
to cusp-free regular bands. While gel concentration affects the speed
of propagation of the wave, it has no effect on its shape or on its
superdiffusive dynamics. Microscopically, we show that the macroscopic
wave propagation and polymorphic transformations are accompanied by
an Ostwald ripening mechanism in which larger red HgI2 crystals
are formed at the expense of smaller yellow HgI2 crystals.