Kinetics induction period

The autoxidation of trilinolein was more complicated than that of the simple fatty esters and did not follow the same rate equation. The order of the reaction was about 0.84 compared to 1.0 for the simple fatty esters. The efficiency of the initiators used, DMVN, was increased to 100% in the trilinolein compared to about 75% in the simple fatty esters. The difference in kinetic behavior between trilinolein and methyl linoleate was attributed to the tendency of the triacylglycerol to form aggregates. The kinetic induction period approach used to measure oxidizability may be subject to errors because of the changes in efficiency of some of the artificial initiators used according to the system and the lipid substrate. Phenolic antioxidants such as a-tocopherol are also affected by the colloidal properties of the lipids used in the oxidation test system employed (Chapter 9). 

The idea of an impurities-driven route had been speculated in prior arts. A mechanism for the initiation of the MTO process by organic impurities instead of any direct route from pure methanol and DME was also suggested [28,87]. Moreover, it was stated that the rate of formation of the initial reaction centers and, therefore, the duration of the kinetic induction period for the first C-C bond formation are governed by impurities [87]. According to Ref. [28], these first hydrocarbons could be the result of impurities present in the MeOH feed or could originate from the incomplete combustion of organic templates from the catalysts, or formed in situ due to, for example, a presence of some transition metal cations on the catalyst, or being formed with the help of the metallic surface of the reactor walls. 

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. 

In addition to the initial reaction between nitric acid and acetic anhydride, subsequent changes lead to the quantitative formation of tetranitromethane in an equimolar mixture of nitric acid and acetic anhydride this reaction was half completed in 1-2 days. An investigation of the kinetics of this reaction showed it to have an induction period of 2-3 h for the solutions examined ([acetyl nitrate] = 0-7 mol 1 ), after which the rate adopted a form approximately of the first order with a half-life of about a day, close to that observed in the preparative experiment mentioned. In confirmation of this, recent workers have found the half-life of a solution at 25 °C of 0-05 mol 1 of nitric acid to be about 2 days. ... 

Kinetic studies involving enzymes can principally be classified into steady and transient state kinetics. In tlie former, tlie enzyme concentration is much lower tlian that of tlie substrate in tlie latter much higher enzyme concentration is used to allow detection of reaction intennediates. In steady state kinetics, the high efficiency of enzymes as a catalyst implies that very low concentrations are adequate to enable reactions to proceed at measurable rates (i.e., reaction times of a few seconds or more). Typical enzyme concentrations are in the range of 10 M to 10 ], while substrate concentrations usually exceed lO M. Consequently, tlie concentrations of enzyme-substrate intermediates are low witli respect to tlie total substrate (reactant) concentrations, even when tlie enzyme is fully saturated. The reaction is considered to be in a steady state after a very short induction period, which greatly simplifies the rate laws. 

The relative fluctuations in Monte Carlo simulations are of the order of magnitude where N is the total number of molecules in the simulation. The observed error in kinetic simulations is about 1-2% when lO molecules are used. In the computer calculations described by Schaad, the grids of the technique shown here are replaced by computer memory, so the capacity of the memory is one limit on the maximum number of molecules. Other programs for stochastic simulation make use of different routes of calculation, and the number of molecules is not a limitation. Enzyme kinetics and very complex oscillatory reactions have been modeled. These simulations are valuable for establishing whether a postulated kinetic scheme is reasonable, for examining the appearance of extrema or induction periods, applicability of the steady-state approximation, and so on. Even the manual method is useful for such purposes. 

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. 

The dependence of reaction rates on pH and on the relative and absolute concentrations of reacting species, coupled with the possibility of autocatalysis and induction periods, has led to the discovery of some spectacular kinetic effects such as H. Landolt s chemical clock (1885) an acidified solution of Na2S03 is reacted with an excess of iodic acid solution in the presence of starch indicator — the induction period before the appearance of the deep-blue starch-iodine colour can be increased systematically from seconds to minutes by appropriate dilution of the solutions before mixing. With an excess of sulfite, free iodine may appear and then disappear as a single pulse due to the following sequence of reactions ... 

Bubbles are formed instantaneously. This conclusion made in [33] is based on estimates taken from earlier works [37]. As seen from the above cited works by S. E. Sosin et al., this is not always true viscoelastic liquids under triaxial stretching stress are not destroyed instantly. The existence of an induction period may produce a considerable effect on foam growth kinetics upon free foaming, when pressure is lowered instantaneously from P > Pcr to P < Pcr in a melt with dissolved gas. However, it would appear that microfaults in polymer melts, which are caused by factors... 

Various investigators have tried to obtain information concerning the reaction mechanism from kinetic studies. However, as is often the case in catalytic studies, the reproducibility of the kinetic measurements proved to be poor. A poor reproducibility can be caused by many factors, including sensitivity of the catalyst to traces of poisons in the reactants and dependence of the catalytic activity on storage conditions, activation procedures, and previous experimental use. Moreover, the activity of the catalyst may not be constant in time because of an induction period or of catalyst decay. Hence, it is often impossible to obtain a catalyst with a constant, reproducible activity and, therefore, kinetic data must be evaluated carefully. 

Fig. 1. Generalized a—time plot summarizing characteristic kinetic behaviour observed for isothermal decompositions of solids. There are wide variations in the relative significance of the various stages (distinguished by letter in the diagram). Some stages may be negligible or absent, many reactions of solids are deceleratory throughout. A, initial reaction (often deceleratory) B, induction period C, acceleratory period D, point of inflection at maximum rate (in some reactions there is an appreciable period of constant rate) E, deceleratory (or decay) period and F, completion of reaction.

The Avrami—Erofe ev equation, eqn. (6), has been successfully used in kinetic analyses of many solid phase decomposition reactions examples are given in Chaps. 4 and 5. For no substance, however, has this expression been more comprehensively applied than in the decomposition of ammonium perchlorate. The value of n for the low temperature reaction of large crystals [268] is reduced at a 0.2 from 4 to 3, corresponding to the completion of nucleation. More recently, the same rate process has been the subject of a particularly detailed and rigorous re-analysis by Jacobs and Ng [452] who used a computer to optimize curve fitting. The main reaction (0.01 < a < 1.0) was well described by the exact Avrami equation, eqn. (4), and kinetic interpretation also included an examination of the rates of development and of multiplication of nuclei during the induction period (a < 0.01). The complete kinetic expressions required to describe quantitatively the overall reaction required a total of ten parameters. 

Magnitudes of n have been empirically established for those kinetic expressions which have found most extensive application e.g. values of n for diffusion-limited equations are usually between 0.53 and 0.58, for the contracting area and volume relations are 1.08 and 1.04, respectively and for the Avrami—Erofe ev equation [eqn. (6)] are 2.00, 3.00 etc. The most significant problem in the use of this approach is in making an accurate allowance for any error in the measured induction period since variations in t [i.e. (f + f0)] can introduce large influences upon the initial shape of the plot. Care is needed in estimating the time required for the sample to reach reaction temperature, particularly in deceleratory reactions, and in considering the influences of an induction period and/or an initial preliminary reaction. 

Having identified the kinetic relation applicable to the data for a particular reaction by the general techniques outlined in the preceding paragraph, it is necessary to confirm linearity of the appropriate plot of the function f(a) against time. The special problems which relate to the induction period, the acceleratory and the deceleratory regions are conveniently considered separately. 

The decomposition kinetics of mercury fulminate [725] are significantly influenced by ageing, pre-irradiation and crushing these additional features of reaction facilitated interpretation of the observations and, in particular, the role of intergranular material in salt breakdown. Following a slow evolution of gas ( 0.1%) during the induction period, the accelerator process for the fresh salt obeyed the exponential law [eqn. (8)] when a < 0.35. The induction period for the aged salt was somewhat shorter and here the acceleratory process obeyed the cube law [eqn. (2), n = 3] and E = 113 kj mole-1. 

The a—time curves for the vacuum decomposition at 593—693 K of lanthanum oxalate [1098] are sigmoid. Following a short induction period (E = 164 kJ mole-1), the inflexion point occurred at a 0.15 and the Prout—Tompkins equation [eqn. (9)] was applied (E = 133 kJ mole-1). Young [29] has suggested, however, that a more appropriate analysis is that exponential behaviour [eqn. (8)] is followed by obedience to the contracting volume equation [eqn. (7), n = 3]. Similar kinetic characteristics were found [1098] for several other lanthanide oxalates and the sequence of relative stabilities established was Gd > Sm > Nd > La > Pr > Ce. The behaviour of europium(III) oxalate [1100] is exceptional in that Eu3+ is readily reduced... 

Recent kinetic studies of this polymerization 14) revealed that some parasitic reactions cause termination and induction periods in the overall process. Their nature is not known yet. It is tentatively suggested that the activated polymers react with the dormant ones yielding some destruction products, although the nucleophile capable of activating the still available dormant chains is regenerated. Alternatively it is possible that the intermediate 3 is labile and may decompose before collapsing into 4 with regeneration of the nucleophile. Whatever the cause of these side reactions, one should stress that the conversion of the monomer into polymer is almost quantitative. 

When two equivalents of pyridine were added to the nmr sample and the probe heated to 80° C, the enol formate 61 decreased and phenyl cyclopropyl ketone 58 appeared at a rate approximately ten times faster than in the previous buffered system. The observation of intermediate 61 and the kinetic results, together with the observed induction periods, are consistent with the idea that some and perhaps all of the rearranged product ketone in the solvolysis of this system arises via double-bond participation in 61 rather than triple-bond participation and a vinyl cation (80). 

The investigators studied various blends of the three polymers in order to control the rate of chain scission and thus influence the induction period and onset of drug release. None of the blends provided the desired 1-week zero-order kinetics. However, blends of different microsphere types did show promise in vitro (88). 

With stannous octoate-promoted polymerization, the metal species is believed to function as the catalyst and water (added or endogenous), or alcohol, serves as the initiator (Fig. 2). This mechanism is supported by recent kinetic studies of PCL polymerization in the presence of triphenyltin acetate (46). After an induction period, polymerization is zero order with respect to monomer and near first... 

The permanganate oxidation of phenols is complicated by the intervention of lower oxidation states of manganese, (c/. the oxidation of toluene, p. 298). For example, the oxidation of 2,6-dinitrophenol in weakly acidic solution displays an induction period, following second-order kinetics thereafter. However, addition of potassium fluoride inhibits reaction almost completely, but manganous ions strongly accelerate it. 

The permanganate oxidation of oxalic acid has been studied exhaustively and has been reviewed by Ladbury and Cullis . It is characterised by an induction period and a sigmoid dependence of rate upon time. Addition of manganous ions eliminates the induction period and produces first-order decay kinetics . Addition of fluoride ions, however, practically eliminates reaction . ... 

---