Activation potentials, kinetic model

Figure 9.8. Effect of catalyst potential Uwr on the apparent activation energy and on the temperature (inset) at which the transition occurs from a high ( ) to a low (O) E value. The dashed lines and predicted asymptotic Ej, E2, E3 activation energy values are from the kinetic model discussed in ref. 11. Conditions p02=5.8 kPa, pCo=3-5 kPa.11 Reprinted with permission from Academic Press.

Accordingly, the potential dependence of the electrode kinetics is determined by the variation of the activation energy with E, which is established by the position of the transition state on the energy profile in Fig. 1.13. This key aspect has been addressed in different ways by the different kinetic models developed. In the following sections, the two main models employed in interfacial electrochemistry will be reviewed. 

To avoid discarding potentially significant information, the parameters obtained fi om isoconversional methods may be used with the original data to determine the kinetic model [49], although this is often not done. Activation energies determined from isoconversional methods [43] are in good agreement with values from isothermal experiments. 

Barrow [772] derived a kinetic model for sorption of ions on soils. This model considers two steps adsorption on heterogeneous surface and diffusive penetration. Eight parameters were used to model sorption kinetics at constant temperature and another parameter (activation energy of diffusion) was necessary to model kinetics at variable T. Normal distribution of initial surface potential was used with its mean value and standard deviation as adjustable parameters. This surface potential was assumed to decrease linearly with the amount adsorbed and amount transferred to the interior (diffusion), and the proportionality factors were two other adjustable parameters. The other model parameters were sorption capacity, binding constant and one rate constant of reaction representing the adsorption, and diffusion coefficient of the adsorbate in tire solid. The results used to test the model cover a broad range of T (3-80°C) and reaction times (1-75 days with uptake steadily increasing). The pH was not recorded or controlled. 

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. ...

This model can be fitted to experimental data, by numerically integrating equation 1 through 3, with the initial condition that for t = 0, the amount of sites of each kind is mao, ruAmo and mm, respectively for the readily active, potentially active and inactive sites. Both the set of kinetic constants, K, ki and k , and the initial condition parameters, Mao, tHAmo and mm, are taken as fitting parameters for each particular experiment. This model can equally be applied to isothermal and to TPR data, provided that a suitable form of variation of the various kinetic constants with ten erature is used. In our case, we assumed that both ky and A, followed an Arrhenius expression and k remained constant. 

Fig. 2). Using these results a kinetics model based on the Arrhenius equation, in which the activation energy was determined from a fitting a Morse potential using the bond dissociation energy determined from the calculations ... 

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