Activation energies distribution

Calculations have been performed for the three reaction mechanisms suggested. The specific temperature-independent rate constants are given in the following table. The parameters Em and activation energy distribution function have been chosen so as to secure the best fit with the exchange data. The ratio iV./iV, was 10-4. 

Fig. 120 Activation energy distributions obtained at - 40 °C (broken line) and 50 °C (solid line) (from [78])...

Let there be the ensemble of particles reacting between themselves under the first-order kinetic law but with differing activation energies of transformation. What will be the shape of the activation energy distribution function of particles if it is known that the distribution function depends on the transformation rate constant according to a hyperbolic law n(k) l/k (kmm< k < Armax) ... 

Table 5.5 Activation energy distribution for kinetic modelling of vitrinite reflectance (EASY%Ro A= 1013s 1 after Burnham Sweeney 1989 Sweeney Burnham 1990)...

This equation was originally developed to express the inactivation kinetics of a-chymotrypsin and glucoamylase covalently bound to a water-insoluble support in an aqueous system (Kawamura et al., 1981). Equation 1.4 was successfully applied to express the oxidation kinetics of fish oil (EPA, eicosapentaenoic acid Yoshii et al., 2003) and linoleic acid powder (Ishidoh et al., 2002, 2003). The above-mentioned three equations are equivalent from the perspective of simulation of flavor release from spray-dried powder. All of the parameters, n in Equation 1.1, (3 in KWW s equation, and a Gaussian distribution with the standard deviation o in Equation 1.4, can be viewed as a consequence of the activation energy distribution of the release rate. 

SuNDARAMAN, P. 1995. Activation-energy distribution—whole-rock versus kerogen. Abstracts of Papers of the American Chemical Society, 209, 18-GEOC. 

As a starting point for the tuning of our multi-component kinetic model we used kinetic data from closed-system non-isothermal pyrolysis experiments which describe the generation of oil and gas from a marine Type II source rock (Dieckmann et al. 1998). The frequency factors (A), activation energy ( ) distributions and hydrocarbon potentials of primary oil and gas generation of Dieckmann et al. (1998) were used as the framework for our model (Figure... 

Fig. 6. Tuned compositional kinetic model, (a) Activation energy distribution as a function ot the total potential, (b) molar composition of the fluid as defined for each E. ...

A new method is described in [91] for the stndy of the nonnniformity of AC. It is based on the mass-spectrometry control of temperature-programmed desorption of prodncts, from the catalyst surface, at the initial stage of the gas-phase polymerisation of olefins. Polymerisation conditions have been selected in a way to favonr the formation of low MW products (up to 14 monomer links in a chain). The anthors report two definite maximums in the areas of 180-210 and 280-320 °C in the process of desorption from the Si02/TiCl4-Al(C2H5)2Cl surface. Therefore, the catalyst contains at least two types of AC with different activation energies of thermal destruction of Ti-C bonds. This publication also contains calculations of the activation energy distribution of thermal Ti-C bond destruction for various types of AC. 

Macdonald [1962] has pointed out that if K(E ) is independent of T, then G(t) cannot be so independent. Both the midpoint To and the width of the distribution will change with temperature. Not all of the G t) proposed in the literature are consistent with this postulate. See Section 2.2.3.S for further discussion of activation energy distributions. 

The clarification of this aspect may have a very significant bearing in catalyst developing, since it is envisaged that it will be possible to predict the behaviour of a particular catalyst by the characterisation of its acid site distribution, which can be obtained using as a practical acidity scale the activation energy distribution obtained by temperature-programmed desorption of bases. 

The abovementioned three equations are equivalent to the perspective of simulating the flavor release from spray-dried powder. All of the parameters - namely n in Avrami s equation, p in the KWW-equation, and a Gaussian distribution of AG with the standard deviation a in Eq. 6.9 - can be understood as a consequence of the activation energy distribution of the release rate. 

This chapter is devoted to an anlaysis of a few ab fine problems of physical chemistry, with a special emphasis on the extraction of the activation-energy distribution from experimental desorption kinetics. 

The activation-energy distribution fi om desorption kinetics (9 versus time t) fi om heterogeneous surfaces. 

In the following, we will try to extract information on the activation-energy distribution from the desorption kinetics more frequently met in practice—the time-logarithm law and the time-power... 

A similar problem is met in adsorption kinetics To which extent do the experimental desorption kinetics 6 t) and the activation energy distribution q> E) specify the kinetic order ... 

Du Z, Saroflm AF, Longwell JP. Activation energy distribution in... modeling and application to the soot-oxygen system. Energy Fuels. 1990 4 296. 

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