Bistable regime

Fig. 49. (a) Local potential drop across the double layer as a function of position and time during a remotely induced transition in the bistable regime of the oxidation of formic acid on a Pt ring electrode. The RE was positioned close to the WE. At the position marked by the arrows the potential was disturbed locally toward positive values. The ring position gives the electrode number of (b). (b) Set-up for measurements used to obtain the data of (a). The outside potential probes serve to measure the local potential the central one serves as the reference electrode. At position 12 is a trigger electrode. (This figure was provided by courtesy of P. Strasser and M. Eiswirth see also Ref. [36].)... 

The experimental results are compiled in Section III.2, which starts with a short description of the methods used to visualize (potential) patterns at electrode surfaces. First wave phenomena in the bistable regime and then in the oscillatory regime are reviewed, with the focal point being on how they fit into the theoretical picture developed in Section III.l. 

With this equation the effect of the location-dependent resistance on the steady states in the bistable regime can be seen easily. The stationary solutions as a function of the radial position are illustrated in Fig. 49(a),... 

Figure 53. Spatiotemporal plot of the local potential during a transition from the passive (low current density) to the active (high current density) state in the bistable regime of the reduction of peroxodisulfate. Circumference of the electrode, 3.46 cm. (After Hatgen and Krischer. )...

Figure 58. Position-time plot of an accelerating front in the bistable regime of Co dissolution. (Reprinted from R. D. Otterstedt, P. J. Plath, N. 1. Jaeger, J. C. Sayer, and J. L. Hudson, Chem, Eng. Sci. 51, 1747, 1996 with kind permission of Elsevier Science Ltd., Kidlington, UK.)...

Regarding the results discussed above, the interesting aspect of these experiments is that the front velocities took on a constant value. Some data can be seen in Fig. 59. The first three examples show activation fronts in the bistable regime of Fe, Au, and Zn dissolution, respectively the last two curves display examples of pulses in an excitable regime, again for metal dissolution reactions, hi all examples, two stationary electrodes were used to probe the local potential. The velocity of the fronts or pulses were extracted from the time difference at which the transitions were measured at the two probes. In all five examples, the readings of the two probes seem to be just time-shifted versions of each other. This indicates that the structures propagate with constant shape and velocity. 

We studied the autocatalytic minimal bromate reaction, which can be oscillatory, but was studied in a bistable regime. A proposed mechanism for this reaction, and participating species, are listed in Table 10.1. 

The net reaction is the oxidation of Ce(III) to Ce(IV) by bromate. In the bistable regime there is a state, where essentially no reaction occurs, which coexists with a state in which a percentage of Ce(III) is oxidized to Ce(IV). In this system we measured [6] at the same time the optical density which gives concentrations of Ce(IV) by Beer s law, and hence also the concentration of Ce(III) by conservation, and the emf of a Pt electrode which at equilibrium follows the Nernst equation (10.1). The experiment consisted of the measurement of the emf of the Ce(III)/Ge(IV) half reaction at a redox (Pt-Ag/AgGl) electrode imder equilibrium and stationary non-equilibrium conditions. The apparatus is shown in Fig. 10.1, but in these experiments the parts 4 7 were not present. From these measurements we determined that there exists a non-Nernstian contribution in a non-equilibrium stationary state as shown in Table 10.2. The concentration of [Ce(III)]ss in the stationary state is obtained... 

The numerical investigation of this equation shows that in the bistable regime the minimum in the diffusional dependence of the transition time between stationary states also occurs Cas in the case of the multivariate master equation ). Fig. 2 shows the results for the Schlogl model Cthe system size is 100 and 200D. 

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