Reactions bistable

For a simple bistable reaction potential, it is clear that maximum curvamre along the reaction pathway will occur near the extrema—the minima and the barrier top. The path endpoints are typically chosen to sit in the reactant and product minima, and in such a case the maximum error will result from the path straddling the barrier top as in Figure 8. Of course, this is the error made in a single segment of the pathway. For a general potential the pathway will consist of multiple segments and may have many barriers. 

Figure 49. (a) N-shaped steady-state polarization curve and different load lines referring to the different effective local electrolyte resistances. The intersections between the polarization curve and load line are stationary states at a certain radial position when the spatial coupling vanishes, (b) Coexisting radial profiles of the double-layer potential at a disk electrode for an electrochemical system with a bistable reaction part. ... 

Based on similar arguments as for the autocatalytic case the width of a filament of the C = 1 state flanked by sharp fronts can be obtained from the balance between the strain A and the propagation speed of the bistable reaction-diffusion front wp ss v/X. By using the expression (4.27), v = (1 — 2a) kD/2, we find for the stable filament solution... 

When this reaction is run in an open system—a so-called continuous-flow stirred tank reactor, or CSTR (fig. 4.4), with continuous influx of reactants and outflow products and unreacted reactants—then for certain influx conditions the system may be in one of two stationary states far from equilibrium one of high I2 concentration, made visibly blue by addition of some starch, and one of low I2 concentration, a colorless solution. Measurements of bistability and chemical hysteresis in this system are shown in fig. 4.5. Bistable reaction systems have some similarities with bistable electronic switches, as pointed out some years ago by Roessler (see cited references in [1-3]). With bistable electronic switches it is possible to build an electronic computer, and now... 

Suppose we take 8 CSTRs, each run as shown in fig. 4.6 with the iodate-arsenous acid reaction, eq. (4.8). Each circle is a CSTR containing this bistable reaction. The arrows indicate tube connections among the 8 tanks through which the reaction fluid from one CSTR is pumped at a set rate into another CSTR. The widths of the lines are a qualitative measure of the rate of transport from one CSTR to another. Each isolated reactor can be in one of two stable stationary states 8 reactors can be in 2 such states. By our choice of the pumping rates we determine how many stable stationary states there are in the coupled reactor system. The dark (white) circles denote a state of high (low) iodide concentration. The choices of pumping rates and stable stationary states... 

Fig. 4.2 Phase portrait for logistic and bistable reaction terms. The front is a heterocUnic saddle-node connection for the logistic case. The front is a saddle-saddle connection for the bistable case...

Rotstein, H.G., Zhabotinsky, A.M., Epstein, I.R. Dynamics of one- and two-dimensional kinks in bistable reaction-diffusion equations with quasi-discrete sources of reaction. Chaos 11(4), 833-842 (2001). http //dx.doi.org/10.1063/1.1418459... 

FIGURE 8.3 The possible movements of the bistable reaction system through the phase space ([Y]ss, A) in the vicinity of the bifurcation points and the corresponding time evolution [Y]ss- The empty circle denotes the starting state of the system [32]. 

The motivation for studying bistable reaction systems came from two different directions. First, a model of a Brownian particle moving in a... 

The investigation of stochastic bistable reactions showed that processes leading to the stationary state might be decomposed in certain situations by... 

Ebeling, W. Malchow, H. (1979). Bifurcations in a bistable reaction-diffusion system. Ann. Physik, 1, Folge, 36, 121-34. 

Ebeling, W. Schimansky-Geier, L. (1979). Stochastic dynamics of a bistable reaction system. Physica, 98A, 587-600. 

Erneux, T. Nicolis, G. 1993. Propagating Waves in Discrete Bistable Reaction-Diffusion Systems, Physica D 67, 237-244. 

Boissonade etal. consider the chemoelastodynamics of responsive gels in Chapter 9. This chapter is devoted to the spontaneous generation of mechanical oscillations by a responsive gel immersed in a reactive medium away from equilibrium. Two important cases are considered. In the first case, the chemomechanical instability is mainly driven by a kinetic instabiUty leading to an oscillatory reaction. The approach is applied to the BZ reaction. The second case is a mechanical oscillatory instability that emerges from the cross-coupUng of a reaction-diffusion process and the volume or size responsiveness of the supporting material. In this case, there is no need for an oscillatory reaction. Bistable reactions, namely, the chlorite-tetrathionate (CT) and the bromate-sulfite (BS) reactions, were chosen... 

An improved model in regard to the simple model presented in Section 9.4.2 has been cut out for more realistic conditions [42]. Not only is the swelling process explicitly tied to an ionic pressure, but there are also other improvements the transport description includes the solvent flow as weU as the dynamics of charged species, the dependence of diffusion coefficients on the gel density is accounted for, and, finally, the kinetic toy model is replaced by a reaHstic model of a spatially bistable reaction. We consider that the functional unit HA of the polyacid has a unique weak-acid function. 

The theoretical study of a bistable reaction in an inhomogeneous medium is a complex but exciting problem because of the large variety of possible behaviours, leading for instance to nucleation processes. The macroscopic analysis is not quite easy, and it does not account for the chemical relaxation between the stable sates. 

AN ELEMENTARY BISTABLE REACTION THE SCHLOGL MODEL 2.1 Schlogl reaction... 

We present here the first experimental demonstration of photochemical bistability in an open reactor. This bistable reaction results from the non-linear properties of a photochromic system the dimer of the triphenylimidazyl radical in chloroform. Hysteresis is observed on the plots of the stationary states of the system over a wide range of flow rates. Within this region, the system is bistable and can be made to flip from one state to the other by an external manipulation. One of the stable states is characterized by a high concentration of violet radicals 2 while in the other the violet radicals are replaced by highly fluorescent compounds. Mechanistic studies showed that this bistability was due to a positive feedback loop. This was thought to arise from the screening effect of the violet radicals 2 with respect to the irradiation of the triphenyl imidazole 3 in combination with an inhibition of the violet radicals 2 by the products of photolysis of triphenylimidazole 3. 

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