Spatial bifurcations of fixed points and limit cycles during the electrochemical oxidation of H2 on Pt ring-electrodes

Abstract

Pattern formation during the oscillatory oxidation of H₂ on Pt ring-electrodes in the presence of electrosorbing ions was studied under potentiostatic control for three different positions of the reference electrode (RE). The position of the RE crucially affects the degree of the global feedback which is imposed by the potentiostatic operation mode, and the three configurations selected corresponded to zero, maximum and intermediate global coupling. In the absence of global coupling, ‘ communication’ among different positions occurs exclusively through migration coupling (the electrochemical counterpart to diffusion in reaction–diffusion systems). In this case, spatially inhomogeneous oscillations that were attributed to a spatial bifurcation of the homogeneous limit cycle were observed throughout. This implies that the system is Benjamin–Feir unstable. For the strongest global coupling adjustable, travelling pulses were found that emerged in a wave bifurcation with n = 1 from the homogeneous steady state. The pulses exhibited modulations in velocity and width that most likely resulted from the interaction between inhomogeneities of the catalytic surface and the nonlinear reaction dynamics. In the case of an intermediate global coupling strength, a diversity of spatio-temporal motions was observed. The dynamics ranged from pulses over target patterns and so-called asymmetric target patterns to mixed states where two or three of these states alternate. For some parameters these mixed states were in addition separated by bursts of the system to a nearly homogeneous unreactive state.