Autocatalytic growth

Bromide ion acts as an inliibitor through step (9) which competes for HBr02 with the rate detennining step for the autocatalytic process described previously, step (4) and step (5). Step (8) and Step (9) constitute a pseudo-first-order removal of Br with HBr02 maintained in a low steady-state concentration. Only once [Br ] < [Br ] = /fo[Br07]//r2 does step (3) become effective, initiating the autocatalytic growth and oxidation. 

Concentration-time curves. Much of Sections 3.1 and 3.2 was devoted to mathematical techniques for describing or simulating concentration as a function of time. Experimental concentration-time curves for reactants, intermediates, and products can be compared with computed curves for reasonable kinetic schemes. Absolute concentrations are most useful, but even instrument responses (such as absorbances) are very helpful. One hopes to identify characteristic features such as the formation and decay of intermediates, approach to an equilibrium state, induction periods, an autocatalytic growth phase, or simple kinetic behavior of certain phases of the reaction. Recall, for example, that for a series first-order reaction scheme, the loss of the initial reactant is simple first-order. Approximations to simple behavior may suggest justifiable mathematical assumptions that can simplify the quantitative description. 

A mechanism based on the continuous formation of seeds and rapid autocatalytic growth has been discussed for the formation of metal nanoparticles including Pt [49]. 

Actually, the kinetics study of the redox potential of transient clusters (Section 20.3.2) has shown that beyond the critical nuclearity, they receive electrons without delay from an electron donor already present. The critical nuclearity depends on the donor potential and then the autocatalytic growth does not stop until the metal ions or the electron donor are not exhausted (Fig. 8c). An extreme case of the size development occurs, despite the presence of the polymer, when the nucleation induced by radiolytic reduction is followed by a chemical reduction. The donor D does not create new nuclei but allows the supercritical clusters to develop. This process may be used to select the cluster final size by the choice of the radiolytic/chemical reduction ratio. But it also occurs spontaneously any time when even a mild reducing agent is present during the radiolytic synthesis. The specificity of this method is to combine the ion reduction successively ... 

Figure 6.15. Schematic of the four-step mechanism for transition metal (e.g., Pt) nanocluster formation. Shown are (i) nucleation to a desired cluster size (ii) autocatalytic growth onto the cluster surface (hi) diffusive agglomerative growth of two nanoclusters and (iv) autocatalytic agglomeration into bulk metal particulates. Reproduced with permission from Besson, C. Finney, E. E. Einke, R. G. J. Am. Chem. Soc. 2005,127, an9. Copyright 2005 American Chemical Society.

Figure 7.4 Snapshots of the spatial distribution for the autocatalytic model (7.1) in the open blinking vortex-sink flow at time intervals equal to the flow period for a supercritical Damkohler number, Da = 7.0. Note, that after a transient time a time-periodic asymptotic state is reached where the autocatalytic growth, localized on the fractal unstable manifold, is balanced by the loss of product due to the outflow from the mixing region, in this case through the point sinks.

As Figure 5 shows, the calculated points agree quite well with the experimental curves. The calculations confirm that the autocatalytic growth of the mass of crystals can take place during the induction period. However, as the absolute quantities of crystals formed during this period are low, they cannot be found by existing methods. 

Figure 6. Transient optical absorption signals of the electron donor decay (reduced form of sulfonato-propyl viologen SPV at 650 nm) and of the autocatalytic growth of silver clusters (at 420 nm), after a critical time. Single pulse in a mixed solution of silver ions and SPY. ...

Pulse radiolysis allows one to observe directly some catalytic electron transfer reactions other than the autocatalytic growth (reactions (25-27). Indeed the clusters are so small that they may be considered as diffusing molecular systems. The electron transfer from MV to protons in water requires the presence of a catalyst, for example radiolytically formed gold or platinum clusters ... 

If the concentration of is high, the reactions depicted by Eqs. (29)-(31) are faster than the coalescence reactions (Eqs. 10 and 11) with a fixed total concentration of atoms and the clusters now grow mostly by successive additions of supplementary reduced atoms (electron plus ion). It has been shown that once formed, a critical cluster, of silver for example,indeed behaves as a growth nucleus. Alternate reactions of electron transfer (Eqs. 32 and 34) and adsorption of surrounding metal ions (Eq. 33) make its redox potential more and more favorable to the transfer (Fig. 8), and autocatalytic growth is observed.The observation of an effective transfer therefore implies that the potential of the critical cluster is at least slightly more positive than that of the electron-donor system, i.e. °(M +/M ) > °(S/S-). 

The possibility of adaptation seems to follow clearly enough from the conclusion that the different enzyme systems obey the law of autocatalytic growth and that when the bacteria are cultured under constant conditions the amounts of the different enzymes settle down to steady ratios. The proportions depend upon the various reaction velocity constants. If something changes the constants, then the proportions should gradually change also. 

In spite of the great number of investigations on CP-driven chemical deposition of metal particles there have been almost no attempts to address the mechanism of this process, either in homogeneous or heterogeneous cases. In a homogeneous system with dispersed metal ions and CP species, the process most probably includes continuous formation of metal nuclei that provide a catalytic surface for further reduction of metal ions and give rise to autocatalytic growth [254]. 

The situation changes significantly in the case of strains like C. necator, where autocatalytic growth of biomass is followed by a phase of linear PHA production. In this case, biomass production should occur in the first step in a CSTR which is coupled to a subsequent plug flow reactor (PFR). The combination CSTR-PFR not only ensures higher productivity, but also minimizes the loss of substrates and co-substrates. Furthermore, product quality can be enhanced by the fact that the PFR features a narrow residence time distribution, leading to higher uniformity of cell populations. This should also have positive impacts on the distribution of the PHA molecular masses and the composition of polyesters [128]. 

Periodic precipitation phenomena, commonly called Liesegang rings, have been studied for a long time. According to recent experimental results (Kai et al., 1982 Muller et al., 1982) patterned precipitation is a postnucleation phenomenon which occurs after a continuous distribution of colloid has been established. The phenomenon can be described at least formally by an instability mechanism based on the autocatalytic growth of colloid particles with diffusion (Ross, 1985). 

The concentration of A is taken as constant, while X, Y, and Z flow in and out of the reactor. Both Y and Z are consumed during the autocatalytic growth of X. In the absence of flow, the system would then shut down once X was consumed by reaction (5.35). If the flow rate and input concentrations are chosen so that Y recovers before Z does, then step (5.34) serves to hold X at a low level until Z increases enough for the cycle to begin again. If the parameters do not yield a sufficient delay, reaction (5.33) resumes too soon for a complete cycle to occur, and the system reaches a steady state with perhaps a few damped oscillations. 

According to the Watzky-Finke model [6], the reactions (6) and (7) correspond to slow continuous nucleation, and fast autocatalytic growth of Au NP s surface, respectively. Using this model, integral kinetic equation of Au NP s formation for isolation conditions (excess of reductant) can be derived ... 

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