Variable activation energy

Activation energies of chemical processes usually amount to tens of kcal/gmol, but those of physical processes such as mass transfer have only a few hundred cal/gmol. Several of the examples of Section P3.06 have variable activation energies. 

FIG. 7-1 Constants of the power law and Arrhenius equations by linearization a) integrated equation, h) integrated first order, (c) differential equation, d) half-time method, e) Arrhenius equation, (/) variable activation energy, and (g) change of mechanism with temperature (T in K). 

The predominance of kinetic studies have assumed uniform sites on the catalyst surface. However, it has long been recognized that many catalyst surfaces exhibit non-uniform sites. Boudart and Djega-Mariadassou [3] have discussed the kinetics of non-uniform surfaces and conclude that "a non-uniform surface behaves catalytically. .like a uniform surface..", and that "rate equations are similar for a given mechanism on a uniform or non-uniform surface". This result justifies "the common practice of neglecting non-uniformity of catalytic surfaces in kinetic studies". However, it appears that uniform catalyst sites catmot adequately explain catalyst deactivation phenomena. The objective of the present study was to explain deactivation in terms of a model based on a variable activation energy site distribution on the catalyst. 

In these expressions we have three potentially variable parameters available for curve fitting Eu b, and AE. For convenience the curve fitting was performed against smoothed data using Fields method of smoothing in which he found he could write his effectively variable activation energy, E, as... 

Vyazovkin, S. (2003). Reply to "What is meant by the term variable activation energy when ap>phed in the kinetics analyses of sohd state decompositions (crystolysis reactions) ", Themochimica Acta, Vol. 397, pp. 269-271 ISSN 0040-6031 Vyazovkin, S. (2010). Thermal Analysis, Analytical Chemistry, Vol. 82, pp. 4936-4949 ISSN 0003-2700... 

Although this relationship is often obeyed, in many cases it is not and the slope changes abruptly [1]. Each different slope has been interpreted to represent a different set of adsorption sites with its own values for Eq and a. However, an alternative perspective of time-dependent adsorption was proposed more recently by Ritchie [15], which in many cases removed the non-linearity observed in Elovich plots. His approach did not necessitate the assumption of a variable activation energy, and he simply assumed that more than one site may be required in the adsorption process. Therefore, the rate of change of surface coverage could be written as ... 

It is generally recognized that the isoconversional methods lead to the dependence of adjustable parameters in the temperature function on conversion. This fact has provided the concept of variable activation energy (see e.g. [496,534] and the references cited therein). As shown in [531], dependence of... 

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