Activation Energy Models

Another approach is known as the Distributed Activation Energy Model (DAEM). This model recognizes that devolatilization occurs through many simultaneous reactions. To express this process in a mathematically tractable manner, these reactions are all presumed to be first order and to be describable by a continuous distribution of kinetic rates with a common pre-exponential and a defined distribution function of activation energy [43],... 

Below 120 K, the temperature dependence of electric conductivity of [N-CH3-Pz](TCNQ) is well approximated by a theoretical curve obtained in the frame of the simple activation energy model ... 

Several versions of coverage-dependent activation energy models with different stoichiometries and functional forms for the coverage dependencies were analyzed by Ivanov et al. (285) in 1980. They analyzed the following general representation of the original mechanism ... 

Fig. 7. Calculated time series for an isothermal coverage-dependent activation energy model showing both sinusoidal (left) and relaxation (right) behaviors. (From Ref. 285.)...

Another model that involves subsurface oxygen was developed by Vish-nevskii for Pt(lOO) (60,70,71). The mathematical formulation, though developed independently, is very similar to that of Bassett and Imbihl, and is also a hybrid between Eigenberger-type models and coverage-dependent activation energy models. This model, however, is in conflict with a surface reconstruction model developed by Ertl et al., which will be discussed later. 

Yet another model previously used to fit the pyrolysis of biomass is the distributed activation energy model. This model was originally used to model the pyrolysis of coal [12], Niksa and Lau [13] found that the distributed activation energy model was the best for coal pyrolysis and that it should be included as an essential element in any pyrolysis model. The pyrolysis is assumed to occur via a number of parallel first order reactions which has the same frequency factor but varying activation energy. The pyrolysis rate for the reactions is ... 

Table 3. Kinetics derived for individual heating rates as well as simultaneously for all three heating rates for the pyrolysis of wheat straw using the distributed activation energy model with 0.055. 

Fig. 5 Pyrolysis of wheat straw at 5, 10 and 40°C/min. Kinetics fitted to the individual curves (A) and simultaneously to three curves (B) by the distributed activation energy model.

J. R. Macdonald, "Generalizations of Universal Dielectric Response and a General Distribution-of-Activation-Energies Model for Dielectric and Conducting Systems," Journal of Applied Physics, 58 (1985) 1971-1978. 

K. Like other superionic conductors, LI TIS. exhibits a prefactor anomaly in the NMR correlation timi, applying a conventional activation energy model for the correlation time... 

In terms of defining end of life wifh 50 % retention, it is challenging to evaluate polymeric compounds for performance at elevated temperatures using the Arrhenius activation energy model when the individual behavior of different compound classes and formulations does not necessarily fit the model. The Arrhenius model may w k very well when the compound exhibits first-order kinetics (Feller, 147). However, plastic compound formulations are complex chemical mixtures of multiple... 

It must be emphasised that the site model is applicable only to relaxation processes showing a constant activation energy, examples being those associated with localised motions in the crystalline regions of semi-crystalline polymers. The temperature dependence of the glass transition relaxation behaviour of polymers does not fit a constant activation energy model, and where this has appeared to be true it is probably a consequence of the limited range of experimental frequencies that were available. 

See, e.g., the formulation and the references in Wattis, J. A. D. Coveney, P. V. Mesoscopic models of nucleation and growth processes a challenge to experiment, Phys. Chem. Chem. Phys. 1999, 1, 2163-2176. This paper draws conclusions from comparisons with experiments for barium sulfate. For an example with organic materials see Burnham, A. K. Weese, R. K. Weeks, B. L. A distributed activation energy model of thermodynamically inhibited nucleation and growth reactions and its application to the P-8 phase transition of HMX, J. Phys. Chem. B 2004,108,19432-19441. 

Activation energy model for grain boundary migration. 

Lakshmanan CC, Bennett ML, White N (1991) ImpUcations of multiplicity in kinetic parameters to petroleum exploration distributed activation energy models. Energy Fuels 5 110-117... 

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