Pseudo Master Curve\nAnalysis of an Infinite Number\nof Parallel First-Order Reactions: Improved Distributed Activation\nEnergy Model

The so-called Distributed Activation Energy Model (DAEM)\nhas been\nused extensively, mainly to analyze pyrolysis reactions of solid reactants.\nThe model expresses many parallel first-order reactions using the\ndistributions of activation energy <i>f</i>(<i>E</i>) and frequency factor <i>k</i><sub>0</sub>(<i>E</i>). Miura and Maki presented a method to estimate both <i>f</i>(<i>E</i>) and <i>k</i><sub>0</sub>(<i>E</i>) in the DAEM in 1998. This model has been used successfully by many\nresearchers. In this paper more general basic equations are derived\nfor describing an infinite number of parallel first-order reactions\nby extending the basic equations for the finite number of parallel\nfirst-order reactions. Revisiting the Miura–Maki method based\non the general basic equations, a graphical analysis method that may\nbe called “Pseudo Master Curve Analysis” is presented.\nThe method not only supplements the Miura–Maki method but gives\nthe underlying concept of the Miura–Maki method clearly. It\nis also shown that the graphical method can be applicable to analyze\nsingle reactions and the experimental data obtained using isothermal\nreaction techniques. Next, a method that improves the estimation accuracy\nof <i>k</i><sub>0</sub>(<i>E</i>) is presented.\nPractical examples analyzing several experimental data are also given\nto show the usefulness and validity of the Miura–Maki method\nand the graphical method. Through the examination, it is proposed\nthat the DAEM should be renamed, for example, as the Distributed Rate\nConstant Model (DRCM).