Estimation of the critical rate of temperature rise for thermal explosion of nitrocellulose using non-isothermal DSC

The expressions to calculate the critical rate of temperature rise of thermal explosion (dT/dt)Tb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} $$\end{document} for energetic materials (EMs) were derived from the Semenov’s thermal explosion theory and autocatalytic reaction rate equation of nth order, CnB, Bna, first-order, apparent empiric-order, simple first-order, Au, apparent empiric-order of m = 0, n = 0, p = 1 and m = 0, n = 1, p = 1, using reasonable hypotheses. A method to determine the kinetic parameters in the autocatalytic-decomposing reaction rate equations and the (dT/dt)Tb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} $$\end{document} in EMs when autocatalytic decomposition converts into thermal explosion from data of DSC curves at different heating rate was presented. Results show that (1) under non-isothermal DSC conditions, the autocatalytic-decomposing reaction of NC (12.97 % N) can be described by the first-order autocatalytic reaction rate equation dα/dt = 1016.00exp(−174520/RT)(1 − α) + 1016.00exp(−163510/RT)α(1 − α); (2) the value of (dT/dt)Tb\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} $$\end{document} for NC (12.97 % N) when autocatalytic decomposition converts into thermal explosion is 0.354 K s−1.