Auto-catalytic kinetics

Cho and Hong (2005) used photodifferential scanning calorimetry to investigate the photocuring kinetics of UV-initiated cationic photopolymerization of 1,4-cyclohexane dimethanol divinyl ether (CHVE) monomer with and without a photosensitizer, 2,4-diethylthioxanthone (DETX) in the presence of a diaryliodonium-salt photoinitiator. Two kinetic parameters, the rate constant (k) and the order of the initiation reaction (m), were determined for the CHVE system using an auto-catalytic kinetics model as shown in the following equation ... 

Abadie et al. (2002) showed that the following auto-catalytic kinetic model was useful for modelling the UV cure of epoxy-resin systems ... 

Thermal treatment, applied to honey, may destroy vitamins and bionutrients, and produce a simultaneous decrease in diastase activity and an increase in HMF content. Honey treatment temperature and time must be limited when pasteurising and stabilising it both diastase activity and HMF content are national and international parameters used as controls so as to limit thermal treatment application. HMF can be formed by hexose dehydration in acid media or by the Maillaid reaction [11,12]. According to Ibarz et al., HMF formation can be described by a second order kinetics (auto-catalytic), with the following equation as expression model [13] ... 

Kinetic data on the thermal degradation of ABS and PC/ABS blends are available (130,131). Thermogravimetric analysis suggests that the kinetics of the thermal degradation can be modelled by an auto-catalytic process. 

Although the simple rate expressions, Eqs. (2-6) and (2-9), may serve as first approximations they are inadequate for the complete description of the kinetics of many epoxy resin curing reactions. Complex parallel or sequential reactions requiring more than one rate constant may be involved. For example these reactions are often auto-catalytic in nature and the rate may become diffusion-controlled as the viscosity of the system increases. If processes of differing heat of reaction are involved, then the deconvolution of the DSC data is difficult and may require information from other analytical techniques. Some approaches to the interpretation of data using more complex kinetic models are discussed in Chapter 4. 

In general it is apparent that these reactions are very complex and precise kinetics cannot be predicted with confidence for given compositions and conditions. The early stages of cure may show auto catalytic features while the onset of gelation can introduce a degree of diffusion-control of the kinetics. Orders of reaction between 0 and 4 have been reported, and the apparent order may change during the reaction. 

Figure 4.7 shows that after reaching the maximum yield the consumption rate of vinylethylbenzenes decreases only slightly. This indicates deficient H202 concentration at the stage of divinylbenzene synthesis. The S-shape of the kinetic curves obtained testifies to the auto-catalytic type of the process with the autoacceleration period from the beginning of these curves to inflection points. 

Without a doubt, these effects deserve further experimental investigation and kinetic analysis. They are not only of interest for the origin of biomolecular homochirality but also as a possible innovation in enantio-selective synthesis, as well as a remarkable example of nonlinear behavior through auto catalytic reaction kinetics. 

According to data of another works the kinetic curve of tumor diameter D change is described by auto-catalytic equation ... 

In view of the fact that the methanol-phenyl isocyanate reaction is known to be an auto-catalytic reaction due to the weakly basic character of the phenylurethane formed, one would expect an upward drift of the second-order plot if the reaction were truly of the second order. This is apparently the case in n-butyl acetate and dioxane. The straight line plot in MEK and acetonitrile and the downward curvature found in toluene and nitrobenzene were taken to indicate an order greater than 2 with respect to the reactants. It appeared that the deviations from second-order kinetics toward higher order in the sequence toluene > nitrobenzene > acetonitrile > MEK > n-butyl acetate > dioxane increased with an increase in the hydrogen bonding capacity of the solvent. 

Process modelling of RTM polyesters was examined by Kenny et al. (1990), who identified the following (auto-catalytic) cure kinetic and (empirical Castro-Macosko (Castro and Macosko 1982) model, as highlighted in (Equation 5.8)) chemorheological models for use in their process simulation ... 

Liu et al. (2004, 2005) examined a three-dimensional non-linear coupled auto-catalytic cure kinetic model and transient-heat-transfer model solved by finite-element methods to simulate the microwave cure process for underfill materials. Temperature and conversion inside the underfill during a microwave cure process were evaluated by solving the nonlinear anisotropic heat-conduction equation including internal heat generation produced by exothermic chemical reactions. 

The model satisfactorily described the cure behavior for the entire range as experimentally monitored by FTIR, DSC, and torsional braid analysis (TBA). This model satisfactorily explained the cure behavior of both catalyzed and uncatalyzed systems over a wide range of temperature and throughout the curing process. The authors proposing the kinetic model considered the reaction to be triggered by the adventitious water and phenol impurities (whose reactions with the cyanate ester is considered as an equilibrium reaction). Catalysis by the added metal ions, which stabilizes the imino carbonate intermediates by complex-ing, is also considered. The model has considered all possible reaction paths and intermediates as detailed in Sect. 4 and depicted in Scheme 14. Considering the various reactions, expressions could be obtained for the individual apparent empirical rate constants of the second order auto catalytic model in terms of the actual rate constants and equilibrium constants. 

The most important fact to remember for the discussion we present in this paper is that, in chemistry, the equation is the complete kinetic equation of the simplest auto-catalytic reaction ... 

In the absence of platinum(II), the Pt(IV) concentration deaeases auto-catalytically, the observed induction period being removed by the addition of bivalent platinum. The reaction is convenient for kinetic study (because of the absence of by-products) and obviously proceeds according to a mechanism similar to that for the oxidation of alkanes. The reaction is first order with respect to the platinum(II) and acetic acid concentrations, and is retarded on the addition of acid and Cl ions, its rate being inversely proportional to the square of chloride-ion concentration at high Cl concentrations. The order of reaction with respect to Pt(IV) changes from 0 to 1. The mechanism suggested for this reaction... 

In the model proposed by Hyver Le Guyader (1990), two systems of equations are considered. In the first version, inactive p34 (i.e. cdc2 kinase) transforms into active p34, either spontaneously or in an auto-catalytic manner active p34 then combines with cyclin to yield active MPF. This situation is described by four differential equations, of a polynomial nature, in which the highest nonlinearities are of the quadratic type. In a second version of this model, governed by three kinetic equations of a similar form, the authors consider the effect of an activation of MPF by MPF itself as well as cyclin, and show that oscillations develop when the degradation of cyclin is brought about by the formation of a complex between cyclin and MPF. That study was the first to show the occurrence of sustained oscillations in a model based on the interactions between cyclin and cdc2 kinase. The type of kinetics considered for these interactions remained, however, remote from the actual kinetics of phosphorylation-dephosphorylation cycles. 

The lr(0) NP catalyzed H/D exchange, in which deuterium incorporation in the 2-H and 4-H positions of the imidazolium occurs only after an induction period (Scheme 6.4). The kinetics are well-fit by the analytical equations corresponding to the auto-catalytic mechanism which is a diagnostic of nanocluster formation [85]. 

Consequently, at intermediate values of conversion, the rate will go through a maximum. At first glance, it might seem that the reaction is auto-catalytic. In reality, it is inhibited by the reactant itself. This unusual result shows the narrow connection between catalysis, autocatalysis and negative catalysis the kinetic patterns are dictated by the reactions with the active centers, their multiplication or their destruction. 

At lower temperatures in the liquid phase, industrial cumene oxidation produces cumene hydroperoxide. In this case, the oxygen bi-radical does not attack the aromatic ring, but rather the activated CH group. The following equation represents the kinetics of the auto-catalytic reaction ... 

M.J.M. Abadie, N.K. Chia F.Y.C. Boey - Cure Kinetics for the Ultraviolet Cationic Polymerization of Cycloliphatic and Diglycidyl Ether of Bisphenol-A (DGEBA) Epoxy Systems with Sulfonium Salt Using an Auto Catalytic Model. J. Appl. Pol)rm. Sc. 7, 86-97 (2002)... 

It is considered in adsorption-autocatalytic theory that the interaction happens at the interface of gas-solid. In some cases, it is foimd that of the auto-catalytic phenomenon happens at the early stages of reduction. The value of this theory indicates the necessity of direct contact of the reductant with metal oxides. It is possible to evaluate the mechanism and kinetics of reduction by use of law of physical chemistry, physics and surface chemistry. The great effect of product (H2O) on the rate of reaction confirms the important role of adsorption. Because H2O is a very active adsorbent, it can occupy the most active areas of oxide, and thus greatly reduce the rate and degree of reduction. 

The use of the new system at ambient pressure and at moderate temperatures allows to follow the reaction kinetics by analysing the concentration of educts and products as a function of time. Batch experiments showed that there is a marked induction period of slow reaction progress (Fig. 18.6) [22, 60, 63]. The systems exhibit the characteristics of an auto-catalytic reaction. Addition of new monomer up to the original starting concentration during the conversion of the monomer does not result in a new induction period but shortly after completion of the reaction the system answers to another addition of monomer with a new induction period [14, 64]. In steady state experiments the polymerization was proceeding over days with constant reaction rate, i. e. without decrease of the catalyst s activity. The re-... 

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