Autocatalytic kinetic behaviour

Products of attack by OH radicals rather than hydrolysis by supercrihcal water occur when 4-nitrophenyl acetate is sonolysed in argon-saturated water. " Hydrolyses of substituted benzoic acid esters in near-critical water (250-300 °C) show autocatalytic kinetic behaviour and surprisingly give the same rate constant regardless of substituent, suggesting that an acid-catalysed mechanism predominates. ... 

The thermal decomposition of AP proceeds to completion in two distinct stages. The low temperature decomposition (420 to 600 K) is an autocatalytic nucleation and growth process. Kinetic behaviour is influenced by a crystallographic transformation (orthorhombic to cubic) at 513 K. Reaction rates just above 513 K are significantly slower than rates immediately below this temperature. The residual... 

It is appropriate to start with BaN6 since this compound has been studied particularly intensively and has been regarded as a model in the development of the theory of kinetics of decompositions of solids. The sigmoid a—time curves for BaN6 pyrolyses, Fig. 15, are typical examples of solid state autocatalytic behaviour. 

The first viewpoint contradicts the autocatalytic character of the reaction, conductometric measurements in the polymerization system and some other facts (see below). Scheme (33) can be considered as completely experimentally substantiated. The following important proofs were obtained A direct experimental discovery of a quaternary ammonium alcoholate in the reaction system, 42) a full agreement of the nature of the active propagating site with all the existing kinetic and structural data l4,149 153 157 I58) establishment of the ionic behaviour of the propagating sites by comparison of the kinetic curves of the process with the character of the electric... 

As well as deceleratory reactions, kineticists often find that some chemical systems show a rate which increases as the extent of reaction increases (at least over some ranges of composition). Such acceleratory, or autocatalytic, behaviour may arise from a complex coupling of more than one elementary kinetic step, and may be manifest as an empirically determined rate law. Typical dependences of R on y for such systems are shown in Figs 6.6(a) and (b). In the former, the curve has a basic parabolic character which can be approximated at its simplest by a quadratic autocatalysis, rate oc y(l - y). 

This situation stems from the peculiarities of the simplest representations of autocatalytic reactions, as discussed previously. In chapter 2, we considered a kinetic scheme in which the autocatalysis proceeded in parallel with an uncatalysed step A - B. We can expect that the inclusion of such a step here will have a strong influence on the behaviour at long residence times, as there will then always be a route from A to B. We consider this in the next section. 

Thus, with the simple cubic autocatalytic rate law, we have been able to find an analytical expression for the time and space dependence of a steady reaction-diffusion wave and make various quantitative and qualitative comments about the behaviour of the wave in terms of the kinetic and diffusion parameters. We now turn to the apparently simpler kinetics of a quadratic autocatalysis, hoping for similar rewards. 

In both these cases there is an autocatalytic element, i.e. one which is both the product of the reaction and which tends to increase its rate. This is the substance B in the first case and heat in the second. It is this element of feedback that is the source of the interesting behaviour. The first two terms in both of these equations represent the access to the site of reaction, in this case the stirred tank, in accordance with the criterion of actuality. The feasibility of these simple reaction schemes can be established by showing that they can be embedded in a fully reversible mechanism and the simple system recovered by limiting processes that do not violate the laws of thermodynamics or kinetics (for example, the Wegscheider condition). Yablonskii and his coworkers (Bykov et al. 1978,1979a, b, c Yablonskii Bykov 1979 Gol dshtein et al. 1986) have considered a number of simple models from which it is clear that the autocatalytic feature is essential. In the bimolecular surface reaction the autocatalytic role is played by the vacant sites which are indeed the product of the main reaction which releases those previously held by adsorbate and, at the same time, are a positive influence on the rate of reaction. 

Using the Tikhonov theorem, the desired behaviour of dynamical system may be modelled or, alternatively, one may obtain from the standard system of chemical kinetics equations (4.27) effective systems of equations which cannot be represented in tms form (for example, of an autocatalytic type or termolecular). 

In their early theoretical studies of the mitotic oscillator, Kauffman et al (Kauffman, 1975 Kauffman Wille, 1975 Tyson Kauffman, 1975) resorted to the abstract, Brusselator model (Lefever Nicolis, 1971) for their simulations of mixing experiments in which Physarum plasmodia taken at different phases of the cell cycle were fused. Like most models proposed for limit cycle behaviour, the Brusselator relies on an autocatalytic step for producing the instability leading to oscillations an advantage of this simple model is that the temporal evolution is governed by two polynomial, nonlinear kinetic equations (Lefever Nicolis, 1971). 

Despite these differences in microscopic behaviour the Kinetics for thermal polymerization are similar in the first three cases with an initially slow rate, followed by an autocatalytic acceleration and a final slow approach to complete conversion. 

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