从DSC曲线数据计算/确定含能材料自催化分解反应动力学参数和热爆炸临界温升速率的方法

为应用热爆炸临界温升速率(dT/dt)_Tb评价含能材料(EMs)的热安全性, 得到计算(dT/dt)_Tb值的基本数据, 用合理的假设, 由Semenov的热爆炸理论和9 个自催化反应速率方程dα/dt=Aexp(-E/RT)α(1-α) (I), dα/dt=Aexp(-E/RT)(1-α)ⁿ(1+K_catα) (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) (VII), dα/dt=A₁exp(-E_a1/RT)+A₂exp(-E_a2/RT)α(1-α) (IX)]导出了计算(dT/dt)_Tb值的9 个表达式. 提出了从不同恒速升温速率(β)条件下的差示扫描量热(DSC)曲线数据计算/确定EMs自催化分解反应的动力学参数和自催化分解转向热爆炸时的(dT/dt)_Tb的方法. 由DSC曲线数据的分析得到了用于计算(dT/dt)_Tb值的β→0 时的onset 温度(T_e0),热爆炸临界温度(T_b)和相应于T_b时的转化率(α_b). 分别用线性最小二乘法和信赖域方法得到方程(I)和(VI)及方程(II)-(V)和方程(VII)-(IX)中的自催化分解反应动力学参数. 用上述基础数据得到了EMs的(dT/dt)_Tb值. 结果表明: (1) 在非等温DSC条件下硝化棉(NC, 13.54% N)分解反应可用表观经验级数自催化反应速率方程dα/dt=10^15.82exp(-170020/RT)(1-α)^1.11+10^15.82exp(-157140/RT)α^1.51(1-α)^2.51描述; (2) NC (13.54% N)自催化分解转向热爆炸时的(dT/dt)_Tb值为0.103 K·s^-1.

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+K_catα) (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) (VII) 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)_Tb 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; (2)The value of for NC (13.54% N) when autocatalytic decomposition converts into thermal explosion is 0.103 K·s^-1.