No abstract

We describe an experimental methodology for the study of chemical self-organization in micropatterned reaction systems. Our approach is based on office-printer-assisted soft lithography and allows the fabrication of centimeter-scale devices with reactor units as small as 50 µm. The devices are made from the elastomeric material poly(dimethylsiloxane) and are filled with a modified Belousov-Zhabotinsky solution. This excitable reaction-diffusion medium employs 1,4-cyclohexanedione as a bubble-free organic substrate and Fe(II)-[batho(SO 3 ) 2 ] 3 as a high-absorbance redox catalyst/indicator. Chemical wave propagation is affected by the loss of bromine from the aqueous phase into the elastomer matrix. The strength of this activating process depends on the local surface-to-volume ratio and can increase the wave velocity by a factor of 2. For devices with gridlike reactor networks, we observe a pronounced deformation of target patterns and the pinning of spiral waves to single elastomer obstacles as well as to obstacle clusters.

Meandering spiral waves are observed in the 1,4-cyclohexanedione Belousov-Zhabotinsky (CHD-BZ) reaction at very low concentrations (3-35 mM) of the organic substrate. The spiral tips describe hypocycle-like trajectories indicating the presence of two main rotation periods and radii. The ratio of these periods approaches 1 for decreasing concentrations of CHD. In this limit, we find Z-shaped trajectories with approximately two lobes. The use of Fe[batho(SO 3 ) 2 ] 3 4-/3-as the BZ catalyst gives rise to extremely long rotation periods (1000-4000 s), and the tip trajectories span large areas of up to 40 mm 2 . As a result of the absence of gaseous products and the high absorption of the catalyst, this particular system is ideally suited for the investigation of spiral waves in closed, thin-layer systems, such as nonuniformly curved and micropatterned media.

We report experimental and numerical results on temporal patterns of propagation failures in reaction-diffusion systems. Experiments employ the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagation failures occur in the frontier region of the wave train and can profoundly affect its expansion speed. The specific rhythms observed vary from simple periodic to highly complex and possibly chaotic sequences. All but the period-1 sequences are found in the transition region between "merging" and "tracking" dynamics, which correspond to wave behavior caused by two qualitatively different types of anomalous dispersion relations.

Meandering spiral tips in homogeneous reaction-diffusion systems are characterized by two generically incommensurate radii and frequencies. Here, we create periodic perturbations in space to induce a transition to commensurate radii and frequencies that exhibit a devil's staircase. The plateaus of the staircase correspond to pinned or complex periodic orbits of the spiral tip.