Pseudo Master Curve Analysis of an Infinite Number of Parallel First-Order Reactions: Improved Distributed Activation Energy Model

The so-called Distributed Activation Energy Model (DAEM) has been used extensively, mainly to analyze pyrolysis reactions of solid reactants. The model expresses many parallel first-order reactions using the distributions of activation energy <i>f</i>(<i>E</i>) and frequency factor <i>k</i> ₀(<i>E</i>). Miura and Maki presented a method to estimate both <i>f</i>(<i>E</i>) and <i>k</i> ₀(<i>E</i>) in the DAEM in 1998. This model has been used successfully by many researchers. In this paper more general basic equations are derived for describing an infinite number of parallel first-order reactions by extending the basic equations for the finite number of parallel first-order reactions. Revisiting the Miura-Maki method based on the general basic equations, a graphical analysis method that may be called "Pseudo Master Curve Analysis" is presented. The method not only supplements the Miura-Maki method but gives the underlying concept of the Miura-Maki method clearly. It is also shown that the graphical method can be applicable to analyze single reactions and the experimental data obtained using isothermal reaction techniques. Next, a method that improves the estimation accuracy of <i>k</i> ₀(<i>E</i>) is presented. Practical examples analyzing several experimental data are also given to show the usefulness and validity of the Miura-Maki method and the graphical method. Through the examination, it is proposed that the DAEM should be renamed, for example, as the Distributed Rate Constant Model (DRCM).