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 f(E) and frequency factor k₀(E). Miura and Maki presented a method to estimate both f(E) and k₀(E) 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 k₀(E) 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).