Tuning the range of spatial coupling in electrochemical systems: From local via nonlocal to global coupling

A specific feature of pattern formation in electrochemical systems is the occurrence of accelerated fronts; they can be attributed to long-range spatial coupling. In this paper we demonstrate that different coupling functions can be realized by tuning easily accessible parameters: The range of the coupling crucially depends on the length scales of the system, and the strength of the coupling is proportional to the conductivity of the electrolyte. Simulations in the bistable regime are presented which illustrate how the front behavior changes qualitatively when length scales or conductivity are varied

Adaptive Method for the Experimental Detection of Instabilities

Motivated by numerical bifurcation detection, we present a methodology for the direct location of bifurcation points in nonlinear dynamic laboratory experiments. The procedure involves active, adaptive use of the bifurcation parameter(s) as control variable(s), coupled with the on-line identification of low-order nonlinear dynamic models from experimental time-series data. Application of the procedure to such “hard” transitions as saddle-node and subcritical Hopf bifurcations is demonstrated through simulated experiments of lumped as well as spatially distributed systems

Adaptive Detection of Instabilities: An Experimental Feasibility Study

We present an example of the practical implementation of a protocol for experimental bifurcation detection based on on-line identification and feedback control ideas. The idea is to couple the experiment with an on-line computer-assisted identification/feedback protocol so that the closed-loop system will converge to the open-loop bifurcation points. We demonstrate the applicability of this instability detection method by real-time, computer-assisted detection of period doubling bifurcations of an electronic circuit; the circuit implements an analog realization of the Roessler system. The method succeeds in locating the bifurcation points even in the presence of modest experimental uncertainties, noise and limited resolution. The results presented here include bifurcation detection experiments that rely on measurements of a single state variable and delay-based phase space reconstruction, as well as an example of tracing entire segments of a codimension-1 bifurcation boundary in two parameter space.Comment: 29 pages, Latex 2.09, 10 figures in encapsulated postscript format (eps), need psfig macro to include them. Submitted to Physica

Breathing Current Domains in Globally Coupled Electrochemical Systems: A Comparison with a Semiconductor Model

Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional domain. The results are compared with the dynamics and the bifurcation scenarios occurring in a closely related model which describes pattern formation in semiconductors. Under galvanostatic control both systems are unstable with respect to the formation of stationary large amplitude current domains. The current domains as well as the homogeneous steady state exhibit oscillatory instabilities for slow dynamics of the potential drop across the double layer, or across the semiconductor device, respectively. The interplay of the different instabilities leads to complex spatio-temporal behavior. We find breathing current domains and chaotic spatio-temporal dynamics in the electrochemical system. Comparing these findings with the results obtained earlier for the semiconductor system, we outline bifurcation scenarios leading to complex dynamics in globally coupled bistable systems with subcritical spatial bifurcations.Comment: 13 pages, 11 figures, 70 references, RevTex4 accepted by PRE http://pre.aps.or

Spatio-temporal pattern formation during the reduction of peroxodisulfate in the bistable and oscillatory regime: a surface plasmon microscopy study

Using surface plasmon microscopy we demonstrate that oscillations as well as transitions in the bistable regime during the reduction of S2O82− at Ag electrodes are accompanied by wave phenomena. Typical velocities of the waves range from some centimeters per second to meters per second, depending on the conductivity of the electrolyte. The characteristic length of the patterns is determined by the temporal dynamics of the potential drop across the double layer at high mass transport and by the dynamics of the concentration of S2O82− at the electrode at low mass transport. The first gives rise to potential fronts with front widths between 0.1 and 0.5 mm; the second leads to smooth structures on the order of centimeters. Further, the influence of the electrode boundary on the pattern formation in electrochemical systems is discussed, as well as the generality of the above-mentioned characteristic times and lengths

Synchronization and Pattern Formation in Electrochemical Oscillators: Model Calculations

There exist many experimental examples of spatial pattern formation in electrochemical systems. Using a recently proposed model, we present numerical simulations of the spatio-temporal behavior in the bistable and oscillatory regime. The simulations reveal that for some parameter regimes only spatially inhomogeneous solutions exist. The impact of the system parameters on the spatial coupling as well as on the existence of patterns is elaborated. The predictions coincide with experimental results for a simple electrochemical reaction, the reduction of peroxodisulfate

The Impact of the Operation Mode on Pattern Formation in Electrode Reactions Prom Potentiostatic to Galvanostatic Control

Applying a constant voltage across an external resistor in series with an electrochemical cell allows the continuous variation of the experimental control mode from potentiostatic to galvanostatic. The model for electrochemical pattern formation presented for potentiostatic conditions in Ref. 1 is extended to account for this general case. The resistor introduces a global coupling into the model, interacting in a nontrivial manner with the nonlocal coupling through migration currents in the electrolyte which occur independently of the control mode. The complex interplay of these two coupling terms is investigated as a function of operating parameters, and is illustrated by simulations in the bistable regime of an electrochemical reaction

Stationary Potential Patterns during the Reduction of Peroxodisulfate at Ag Ring Electrodes

The potential distribution in front of a Ag ring electrode during the reduction of peroxodisulfate was measured with potential microprobes. Inhomogeneous stationary potential distributions were observed when using a Haber−Luggin capillary, i.e., placing the reference electrode close to the working electrode on the axis of the ring. It is shown that such an arrangement introduces a negative global coupling into the system which destabilizes homogeneous stationary states if the current−potential characteristics exhibits a negative differential resistance. Further consequences of the negative global coupling are discussed, and the effect of an additional, external series resistor is demonstrated