Autocatalytic species

An experimental test for autocatalysis involves addition of the suspected autocatalytic species to the reaction mixture. If the material added is the responsible agent, one may generally expect behavior like that shown in Figure 9.14. 

By noting that the temperature rise in this system takes the feedback role that was played by the autocatalytic species B in the previous chapter, we may recognize the resemblance between the rate constant k2 of the previous chapter (rate constant for decay of B) with l/rN here (a pseudo-rate constant for decay of the temperature rise). For a system in which heat transfer is slow, fN will be large if heat transfer across the surface is rapid, tN will be small. The dimensionless time, therefore, becomes... 

Figure 6.6(b) is better approximated by a cubic form, rate ocy2(l — y). Cubic autocatalysis has already provided us with behaviour of interest in chapter 2. In the remainder of this chapter we consider the stationary-state responses of schemes with this feedback mechanism in flow reactors. We will consider three models, with increasingly varied possible behaviour first an autocatalytic step on its own next we allow the autocatalytic species to undergo a subsequent reaction finally we add an uncatalysed reaction in competition with the autocatalysis. The local stability of such systems is... 

In the previous sections, the autocatalytic species B is only removed from the reactor by means of outflow or by conversion back to the original reactant A. We now consider the case where B can undergo an additional decay process, B - C, similar to that considered in the model of chapter 2. Returning to irreversible steps, the kinetic scheme becomes, for autocatalysis,... 

Thus the two loci cross at some point provided fi is greater than unity. Any inequality in the diffusion coefficients, in favour of the non-autocatalytic species, can support pattern formation over some range of experimental conditions. 

The origin of the various additive effects is still unknown. However, taking into account the wide variety of chiral additives that cause effects with considerable sensitivity, it can be assumed that unspecific rather than specific interactions between the additives and species involved in the reaction mechanism of the Soai reaction take place. These may cause small but directed chiral perturbations where advantage is taken of the extraordinarily strong autocatalytic amplification capacity of the system. As already demonstrated by Singleton and Vo [36], these perturbations can be extremely small without losing its enantiomeric direction. In fact, as we describe later, the assumption of interactions between these chiral additives and the Soai reaction product itself, i.e., the autocatalytic species, could provide a tentative explanation for such effects. 

During classical asymmetric synthesis, the amplitude of these fluctuations are expected to decrease during the course of the reaction because more and more chiral molecules are formed and eeeXp declines. However, in the presence of chiral autocatalysis, the small ee caused by such fluctuations can be amplified. In such cases, the system is likely to be most sensitive in the initial stage of reaction when the concentration of chiral molecules is still small. If the autocatalytic species are concentrated they can be either in a racemic or optically active state but if they are highly diluted, as at the beginning of the reaction, statistical fluctuations can become significant so that the state... 

If a second variable participates in an additional feedback loop with a negative regulation, oscillations become possible. The mutual dependencies of the two variables, which have been coined activator and inhibitor, are depicted in Fig. 1. A, the autocatalytic species is the activator it activates the production of /, and I is the inhibitor because it slows down or inhibits the growth of A [13, 14]. Oscillations arise in activator-inhibitor systems if characteristic changes of the activator occur on a faster time-scale than the ones of the inhibitor. In other words, the inhibitor must respond to a variation of the activator variable with some delay. In fields as diverse as semiconductor physics, chemistry, biochemistry or astrophysics, and also in electrochemistry, most simple periodic oscillations can be traced back to such an activator-inhibitor scheme. 

In a parallel reaction the adsorbate, OHad, acts as a catalyst for the H202 reduction and is thus an autocatalytic species ... 

In category 1, the order of the autocatalytic species in the cycle reaction is equal to one (and equal to the order of X in the exit reaction). Category 2 oscillators include mechanisms with autocatalytic reaction of a higher (effective) order in X than the order of X in the removal reaction, and the type X species need not necessarily be chemical species. Rather, they may include vacant surface sites in heterogeneous catalysis, or temperature in thermokinetic oscillation. 

The expressions for the trace T and the determinant A in terms of e, q, and h are somewhat lengthy and not enlightening. They are best evaluated for specific values of the parameters. The Oregonator also belongs to the class of pure activator-inhibitor systems. The autocatalytic species HBr02 is the activator and the oxidized catalyst the inhibitor. 

B-Z reaction using ferroin as a catalyst has been used for pattern formation studies for such a system. According to FKN mechanism, HB1O2 is the autocatalytic species. On commencement of autocatalysis the [Br ] is depleted to a value lower than the critical value. The autocatalytic production of HBrOj is accompanied by oxidation of ferroin to firrin Fe(phen3) +. Br formation occurs due to reaction of Fe(phen3) with bromo-malonic acid. Thus, a differential flow between HBr02 and Br can be achieved. 

It is believed that LiPF -based electrolytes react with water by the following reac-tions and the produced HF affects the nature of SEI on the electrodes. It was reported that the addition of LiCl and HMPA in LiPF electrolytes suppressed the hydrolysis reaction and thermal decomposition, " respectively. A Lewis base, which can complex PF to form a stable acid-base adduct, should prevent the generation of the autocatalytic species. 

The first term of the rate law is concerned with the production of the autocatalytic species [Rh(CO)2Cl2], for which equation (156) represents the proposed mechanism. Further production of Rh(I) is autocatalytic due to an efficient reduction pathway which is thought to proceed through a [Rh - - - -Cl-Rh ] bridged species, equa-... 

This equation can be solved either analytically or numerically to yield the curve in Figure 2.1, which shows the typical explosion in the concentration of the autocatalytic species I. ... 

The first term is concerned with the initial rate while the second is a contribution from an autocalalytic reaction which becomes dominant as the carbonylation progresses. The step in the reaction to give the autocatalytic species [Rh(CO)2-Brg]" involves a reductive carbonylation process via a carboxylate intermediate (Scheme 14). This assumes that co-ordinated HgO or OH is involved in the reaction and migrates to a cis carbonyl. External HgO/OH attack is also feasible but is considered less probable in view of previous observations that oxidation of ethylene to acetaldehyde using [RhClji(HaO)6-n] complexes does not occur when n=6, i.e. when co-ordinated HgO is not present. A comparison of kinetic data for the bromide with those of [RhCl6(H20)] indicates that the former is some thirty... 

The motion of the polymeric network was obtained in numerical simulations by a multistep finite difference method from Eq. (9.26). In Figure 9.3(a), we show oscillations, obtained for appropriate parameters. In (b), we show the concentration distributions of the autocatalytic species for the same intermediate value of the sphere radius Rs = 5 taken, respectively, when the system is swelling (F state) or shrinking (FT state). 

The mechanisms of sulfur oscillators remain a mystery at this time. Even the autocatalytic species, if any, has yet to be identified. 

The oxidized chemical waves themselves are a consequence of the coupling between diffusion and chemical reaction. Their velocity is determined by the diffusion coefficient of the autocatalytic species HBrO and the rate constant of its formation in the autocatalytic reaction mentioned above ... 

As the concentration of the autocatalytic species in the inflow increases, the two tangents move closer together. The range of over which hysteresis occurs decreases. When... 

Here c denotes the velocity of plane waves and D represents the diffusion coefficient of the autocatalytic species. The relationship predicts a minimum radius i crit = D/c below which propagation of circular waves will not take place. With the computerized video techniques it is possible to measure the negative curvature of the narrow cusps as a function of time. The analysis yields a value of Z) 2.0 x 10 cm /s [37], which is a good approximation of the diffusion coefficient of the autocatalytic species HBr02. Equation (2) plays an important role for the dynamics of the highly curved tip of the spiral. 

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