Method to determine the kinetic parameters of the autocatalytic decomposition reaction and critical rate of temperature rise of thermal explosion of energetic materials from DSC curves

To evaluate the thermal safety of energetic materials (EMs) using the critical rate of temperature rise of thermal explosion (dT/dt)_Tb and obtain basic data used to calculate (dT/dt)_Tb, nine expressions to calculate (dT/dt)_Tb for EMs were derived from Semenov thermal explosion theory and nine autocatalytic reaction rate equations, dα/dt=Aexp(-E/RT)α(1-α) (I), dα/dt=Aexp(-E/RT)(1-α)ⁿ(1+Kcatα) (II), dα/dt=Aexp(-E/RT) [α^a-(1-α)ⁿ] (III), dα/dt=A₁exp(-E_a1/RT) (1-α) + A₂exp(-E_a2/RT) α(1-α) (IV), dα/dt= A₁exp(-E_a1/RT) (1-α)^m + A₂exp(-E_a2/RT)αⁿ(1-α)^p (V), dα/dt=Aexp(-E/RT) (1-α) (VI), dα/dt=Aexp(-E/RT) · (1-α)ⁿ (VII), dα/dt=A₁exp(-E_a1/RT)+A₂exp(-E_a2/RT)(1-α) (VIII) and dα/dt=A₁exp(-E_a1/RT)+A₂exp(-E_a2/RT)α· (1-α) (IX), using reasonable hypotheses. A method to determine the kinetic parameters in the nine autocatalytic decomposition reaction rate equations and (dT/dt)_Tb of EMs when autocatalytic decomposition converts into thermal explosion from difference scanning calorimetry (DSC) curves at different heating rates (β) was presented. The onset temperature (T_e0) corresponding to heating rate β →0, the critical temperature of thermal explosion (T_b) and the conversion degree (α_b) corresponding to T_b used in the calculation of (dT/dt)T_b were obtained from analysis of DSC curves. The kinetic parameters of the autocatalytic decomposition reactions in Eqs.(I) and (VI), and Eqs.(II)-(V), (VII)-(IX) were estimated by the linear least-squares method and trust region approach, respectively. The values of (dT/dt)_Tb for EMs were obtained from basic DSC data. Results show that (1) under non-isothermal DSC conditions, the autocatalytic decomposition reaction of nitrocotton (NC) (13.54% N) can be described by the apparent empiric-order equation dα/dt=10^15.82exp(-170020/RT) (1-α)^1.11 +10^15.82exp(-157140/RT)α^1.51(1-α)^2.51, and (2) the value of (dT/dt)_Tb for NC (13.54% N) when autocatalytic decomposition converts into thermal explosion is 0.103 K·s^-1.