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 $ ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} $ for energetic materials (EMs) were derived from the Semenov’s thermal explosion theory and autocatalytic reaction rate equation of nth order, C_nB, B_na, first-order, apparent empiric-order, simple first-order, A_u, 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 $ ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} $ 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 = 10^16.00exp(?174520/RT)(1 ? α) + 10^16.00exp(?163510/RT)α(1 ? α); (2) the value of $ ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} $ for NC (12.97 % N) when autocatalytic decomposition converts into thermal explosion is 0.354 K s^?1.