Autocatalytic order

Often biological or biochemical functions are not realized over all the time throughout the lifecycle of some organism but rather operate for limited times and occasions such as reproduction, metamorphosis (role of iodine in amphibia), synthesis of hormons or other signaling components or of anti-eating poisons or repellants or detoxification agents like metallothion-eins. In such cases, the autocatalytic order related to... 

Although it was that simple to derive the rule of three functions in biochemistry in general, this modification cannot be calculated as straightforwardly because the reduction of autocatalytic order due to oligomerization depends sensitively on (bio-)chemical network topology. In addition to topological aspects of feedback in the network, the exact kind (manner) of dimerization which interconnects identical metal ions needs to be known, likewise the way by which the substrate interacts with this multimetal center (for example, the Mo dimerization effect is also seen with Mo-dependent nitrogenases but and the other reduc-... 

Hitherto certain metals which are known to be essential were discussed with respect to their matter flow rates, sources, sinks and autocatalytic orders, using Eq. 2.4 as a kind of background information to... 

The Landolt reaction (iodate + reductant) is prototypical of an autocatalytic clock reaction. During the induction period, the absence of the feedback species (Irere iodide ion, assumed to have virtually zero initial concentration and fomred from the reactant iodate only via very slow initiation steps) causes the reaction mixture to become kinetically frozen . There is reaction, but the intemiediate species evolve on concentration scales many orders of magnitude less than those of the reactant. The induction period depends on the initial concentrations of the major reactants in a maimer predicted by integrating the overall rate cubic autocatalytic rate law, given in section A3.14.1.1. 

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. 

At relatively low temperatures, the effect of added nitric acid was to catalyse the reaction strongly, and to modify it to the autocatalytic form. At higher temperatures the effect of this additive was much weaker, as was the induced autocatalysis. Under these circumstances the catalysis was second-order in the concentration of nitric acid, and the presence of 0-25 mol l i of it brought about a sixfold change in the rate. 

Thermal stabihty of the foaming agent in the presence of high temperature steam is essential. Alkylaromatic sulfonates possess superior chemical stabihty at elevated temperatures (205,206). However, alpha-olefin sulfonates have sufficient chemical stabihty to justify their use at steam temperatures characteristic of most U.S. steamflood operations. Decomposition is a desulfonation process which is first order in both surfactant and acid concentrations (206). Because acid is generated in the decomposition, the process is autocatalytic. However, reservoir rock has a substantial buffering effect. 

Kinetics are slow and many hours are requited for a 95% conversion of the reactants. In the case of the subject compound, there is evidence that the reaction is autocatalytic but only when approximately 30% conversion to the product has occurred (19). Reaction kinetics are heavily dependent on the species of halogen ia the alkyl haHde and decrease ia the order I >Br >C1. Tetrabutylphosphonium chloride exhibits a high solubiHty ia a variety of solvents, for example, >80% ia water, >70% ia 2-propanol, and >50% ia toluene at 25°C. Its analogues show similar properties. One of the latest appHcations for this phosphonium salt is the manufacture of readily dyeable polyester yams (20,21). 

Electroless Electrolytic Plating. In electroless or autocatalytic plating, no external voltage/current source is required (21). The voltage/current is suppHed by the chemical reduction of an agent at the deposit surface. The reduction reaction must be catalyzed, and often boron or phosphoms is used as the catalyst. Materials that are commonly deposited by electroless plating (qv) are Ni, Cu, Au, Pd, Pt, Ag, Co, and Ni—Fe (permalloy). In order to initiate the electroless deposition process, a catalyst must be present on the surface. A common catalyst for electroless nickel is tin. Often an accelerator is needed to remove the protective coat on the catalysis and start the reaction. 

Organic Solids A few organic compounds decompose before melting, mostly nitrogen compounds azides, diazo compounds, and nitramines. The processes are exothermic, classed as explosions, and may follow an autocatalytic law. Temperature ranges of decomposition are mostly 100 to 200°C (212 to 392°F). Only spotty results have been obtained, with no coherent pattern. The decomposition of malonic acid has been measured for both the solid and the supercooled liquid. The first-order specific rates at 126.3°C (259.3°F) were 0.00025/min for solid and 0.00207 for liquid, a ratio of 8 at II0.8°C (23I.4°F), the values were 0.000021 and 0.00047, a ratio of 39. The decomposition of oxalic acid (m.p. I89°C) obeyed a zero-order law at 130 to I70°C (266 to 338°F). 

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. 

Torkar et al. [702,706—708] identified nucleation as an autocatalytic process at the (hk0) planes of hexagonal platelets of NaN3. The decelera-tory reaction fitted the first-order equation [eqn. (15)]. Values of E tended to be irreproducible for the pure salt E was about 180 kJ mole 1 but this was reduced to about half by doping. This influence of an additive and the observed similarities in magnitudes of E for decomposition and for diffusion were interpreted as indicating that growth of nuclei was controlled by a diffusion process. 

A review of epoxy-novolac reaction mechanisms and kinetics is provided by Biernath et al.85 Depending on the structures of the novolac and the epoxy, reactions have been reported to proceed through an nth-order mechanism or an autocatalytic mechanism.88-92... 

Since the autocatalytic reaction is third order, a steady-state material balance gives a cubic in bout- This means there are one or three steady states. Suppose binjain = 1/15 and explore the stability of the single or middle steady state for each of the following cases ... 

The oxidation of di-2-chloroethyl ether is first-order with respect to ether, but is autocatalytic and chloride ion is liberated. A hydrogen atom abstraction process, similar to that above, probably takes place, viz. 

Regions of stable and unstable operation determined by numerical simulation of mass and heat balances equations first- and second-order, autocatalytic, and product-inhibited kinetics graphically presented boundaries in co-ordinates in practice. safe operation if l/5e>2. Equality of heat generation and heat removal rates Semenov approach modified for first-order kinetics. 

An autocatalytic reaction does not necessarily imply a first-order dependence on the product species, or even an integer order with respect to... 

In a self-reproducing, catalytic hypercycle (second order, because of its double function of protein and RNA synthesis) the polynucleotides Ni contained not only the information necessary for their own autocatalytic self-replication but also that required for the synthesis of the proteins Ei. The hypercycle is closed only when the last enzyme in the cycle catalyses the formation of the first polynucleotide. Hypercycles can be described mathematically by a system of non-linear differential equations. In spite of all its scientific elegance and general acceptance (with certain limitations), the hypercycle does not seem to be relevant for the question of the origin of life, since there is no answer to the question how did the first hypercycle emerge in the first place (Lahav, 1999). 

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