Autocatalytic course

In aqueous solution the catalytic esterolyses with polymeric catalysts is accelerated by hydrophobic bonding . The catalytic effect of synthetic polymers on hydrolysis has been reviewed by Kunitake and Okahata (57). Linear polyvinylimid-azole (Scheme 5) increases the rate of hydrolyses of 3-nitro-4-acyloxybenzoic acid by a factor of 103 with respect to monomeric imidazole 58-62). The primary reaction is the acylation of polyvinylimidazole. The effect is dependent on chain length of the acid and the solvent. The hydrophobic interaction causes an autocatalytic course of reaction rate. The acylated polyvinylimidazole is more hydrophobic than the starting polymer. At a 75% conversion the rate is five times higher than the initial rate. 

In the given example the autocatalytic course of the reaction is consistent with its mechanism. However, in the overwhelming majority of cases the reaction mechanism and the kinetic equation have nothing in common. It has been shown that autocatalysis of the kind... 

Figure 2.4 illustrates the course of the reaction for various values of bolao. Inflection points and S-shaped curves are characteristic of autocatalytic behavior. The reaction rate is initially low because the concentration of the catalyst, B, is low. Indeed, no reaction ever occurs if bo = 0. As B is formed, the rate accelerates and continues to increase so long as the term ab in Equation (2.28) is growing. Eventually, however, this term must decrease as component A is depleted, even though the concentration of B continues to increase. The inflection point is caused by depletion of component A. 

Processes are called autocatalytic if the products of a reaction accelerate their own formation. Autocatalytic reactions get faster as the reaction proceeds, sometimes dramatically, sometimes slowly and steadily. Exponential growth is a very basic non-chemical example. Of course the acceleration cannot be permanent the reaction will slow down and eventually come to an end once the starting materials have been used up. Only economists believe in sustainable growth. 

The time-course of an autocatalytic process. Note that during the early stages the amount of active catalyst is low, but changes dramatically as a function of time. 

It is of course surprising that amino acids can be obtained via the Strecker synthesis, purines from the condensation of HCN, pyrimidines from the reaction of cyanoacetilene with urea, and sugars from the autocatalytic condensation of formaldehyde. The synthesis of chemical constiments of contemporary organisms by non-enzymatic processes under laboratory conditions does not necessarily imply that they were either essential for the origin of life or available in the primitive environment. However, the significance of prebiotic simulation experiments is... 

The time course of an actual experiment is shown in Figure 7.17, which shows the hydrolysis of oleic anhydride catalyzed by spontaneously formed oleate vesicles. Note the sigmoid behavior, typical of an autocatalytic process. The lag phase is due to the preliminary formation of vesicles, and in fact the length of the lag phase is shortened when already formed vesicles are pre-added, as shown in the hg-ure. Some mechanistic details of these processes will be discussed in Chapter 10. In this work, an analysis of the number and size distribution of vesicles at the beginning and the end of the reaction was also performed by electron microscopy. 

In this simplified version of the Brusselator model, the trimolecular autocatalytic step, which is a necessary condition for the existence of instabilities, is, of course, retained. However, the linear source-sink reaction steps A—>X—>E are suppressed. A continuous flow of X inside the system may still be ensured through the values maintained at the boundaries. The price of this simplification is that (36) can never lead to a homogeneous time-periodic solution. The homogeneous steady states are... 

Activation of prochymosin involves the splitting of peptides from the N-terminal end of prochymosin with simultaneous reduction in molecular weight from about 36,000 to 31,000. The rate of conversion increases markedly with decreasing pH below 5.0 (Rand and Emstrom 1964). At pH 5.0, NaCl concentrations up to 2M increase the rate of activation. Milk-clotting activity plotted against activation time at pH 5.0 shows the course of activation (Fig. 12.1) to be autocatalytic. If activation is carried out in the presence of preformed chymosin, the S-shape disappears and the initial rate of the activation process increases with increasing concentration of preformed chymosin. Folt-... 

For most reactions, the rate decreases as the reaction proceeds (important exceptions being a number of biological reactions which are autocatalytic). For a reaction with no volume change, the rate is represented by the slope of the curve of X (moles converted per unit volume) versus time (Fig. 1.10), which decreases steadily with increasing time. The maximum reaction rate occurs at zero time, and, if our sole concern were to obtain maximum output from the reactor and the shutdown time were zero, it appears that the best course would be to discharge the reactor after only a short reaction time tr, and refill with fresh reactants. It would then be necessary, of course, to separate a large amount of reactant from a small amount of product. However, if the shut-down time is appreciable and has a value ts then as we have seen in the example on ethyl acetate above, the average production rate per unit volume is ... 

As has already been indicated, longitudinal heat transfer and diffusion in a detonation wave may be disregarded so that the chemical reaction runs almost adiabatically. In the case of an autocatalytic reaction, the absence of diffusion of the catalyzing products may significantly delay the flow of the reaction in the detonation wave. In the course of reaction along the Todes line, the heat release is tied to a significant increase in temperature. 

A reaction is called autocatalytic, when a reaction product acts as a catalyst on the reaction course [3]. 

Figu re 12.1 Comparison of autocatalytic (a) an nth-order (ri) reactions in an isothermal DSC experiment performed at 200°C. Both reactions present a maximum heat release rate of lOOWkg 1 at 200°C. The induction time of the autocatalytic reaction leads to a delay in the reaction course. 

Different factors may strongly affect the behavior of autocatalytic reactions, especially if we consider the adiabatic temperature course that is used to predict the TMRad. Such effects are shown by numerical simulations using the Berlin model. 

Figure 12.11 Adiabatic temperature course of an autocatalytic reaction (solid line) compared to the zero-order approximation (dashed line). Both reactions have a maximum heat release rate of lOOWkg-1 at 200°C and an energy of500)g . ...

Table 1 Solvent effects on the course of autocatalytic reaction between the methylpyrim-idinal and diisopropylzinc...

In the course of NMR studies of the autocatalytic system in CyDg, several experiments were carried out in which the 2-TMS-alkynylpyrimidine-5-aldehyde was directly mixed with diisopropylzinc at low temperatures and allowed to warm until the reaction was complete. The dimeric product can then be observed directly, and would be expected to be racemic since there are no internal or external chiral influences on the reaction. This was not the case, and an imbalance in favour of the homochiral form was sometimes observed a striking example is shown in Fig. 17. Since there is no workup... 

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... 

Another scenario for the origin of homochirality was suggested by Pearson [8,9] such that chance breaks the chiral symmetry. Though the mean number of right- and left-handed enantiomers are the same, there is a nonzero probability of deviation from the equal populations of both enantiomers. The probability of establishing homochirality in a macroscopic system is, of course, very small [10], but chance produces a slight majority of one type of enantiomer and asymmetric compounds when they have once arisen act as breeders, with a power of selecting their own kind of asymmetry form [8,9]. In this scenario, produced enantiomer acts as a chiral catalyst for the production of its own kind and hence this process should be autocatalytic. 

Food lipids possess an inherent stability to oxidation, which is influenced by the presence of antioxidants and pro-oxidants. After a period of relative stability (induction period), lipid oxidation becomes autocatalytic and rancidity develops. Thus, the typical time-course of autoxidation, as measured by the concentration of hydroperoxides, consists of a lag phase (induction) followed by the rapid accumulation of hydroperoxides, which reaches a maximum and then decreases as hydroperoxide decomposition reactions become more important. The longer the induction period, the more stable the food to oxidation (Lundberg, 1962). 

In this cycle, the main feature is that template T can bind to itself by complementary supramolecular binding units, thus autocatalytically increasing its concentration during the course of the reaction. In a first step, T reversibly binds its constituents A and B to yield a termolecular complex M. This complex pays the entropy penalty that brings the two precursors into close proximity, which facilitates the formation of a covalent bond between them, whether or not this one is assisted by an enzyme [34]. In a second step, termolecular complex M is... 

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