# Modeling of Impact Energy Release of PTFE/Al Reactive Material
## 2 Modeling of PTFE/Al Impact Energy Release
### Parameters Determination of Reaction Rate Equation  
The mechanistic interpretations of solid-state kinetics are based on the concept of a single-step reaction as given by [29]:  
\[\frac{dy}{dt}=k(T)f(y) \tag{22}\]  
In the formula, \(y\) is the degree of chemical reaction, \(t\) is the time, \(k(T)\) is the temperature relationship of the rate constant, and \(f(y)\) is the reaction mechanism function. [PERSON] proposed the rate constant-temperature relationship by simulating the equilibrium constant-temperature relationship:  
\[k(T)=A_{0}\exp(-\frac{E_{a}}{R_{u}T}) \tag{23}\]  
In the formula, \(E_{a}\) is the activation energy, \(A_{0}\) is the pre-exponential factor, \(T\) is the temperature, and \(R_{u}\) is the gas constant. In order to have a similar form to the rate equation of the trinomial ignition state equation, the Manpel reaction model was selected, and \(f(y)\) is the following formula:  
\[f(y)=1-y \tag{24}\]  
Put \(k(T)\) and \(f(y)\) into Equation (23) to get Equation (25):  
\[\frac{dy}{dt}=A_{0}\exp(-\frac{E_{a}}{R_{u}T})(1-y) \tag{25}\]  
When the temperature is known, there are only two unknown constants in Equation (26). If \(A_{0}\), \(E_{a}\), and the initial temperature are known, the reaction degree of the reactive material \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**A (Mbar)** & **B (MBar)** & **R1** & **R2** & **\(\mathbf{\omega}\)** \\ \hline
0.2195 & 0.0166 & 4.420 & 1.495 & 0.006 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: JWL equation of state parameters for PTFE/Al reaction products. Figure 2: \(\gamma\) state equation curve and JWL curve of PTFE/Al products. at the end of the reaction can be calculated. [PERSON] [15] obtained the reaction degree of the PTFE/Al reactive fragments under different impact pressures through the impact energy release experiments. Table 5 records the reaction degree and impact pressure of 20 groups of experiments, and Figure 3 shows the relationship between the reaction degree and the impact pressure. In the process of heat transfer between PTFE/Al and air, Equation (26) is assumed to calculate the decrease in temperature of the reactive material:  
\[\Delta T=C(T-T_{0}) \tag{26}\]  
In the formula, \(C\) is a constant, \(T\) is the current temperature, and \(T_{0}\) is the initial temperature. The relationship between the collision pressure and the reaction degree of PTFE/Al in Table 5 was used to determine the parameters of the reaction rate equation. The specific steps are as follows:  
1. The shock temperature corresponding to the shock pressure was calculated by Equation (21), and the relationship between impact temperature and reaction degree was obtained. 2. \(A_{0}\), \(E_{a}\), and \(C\) were selected within the given range. 3. The reaction rate of the PTFE/Al reactive material at the current temperature was calculated through Equation (25). Figure 3: The corresponding relationship between collision pressure and reaction degree. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Collision Pressure** & **Reaction** & \multirow{2}{*}{**Number**} & **Collision Pressure** & **Reaction** \\  & **(Gpa)** & **Degree** & & **(Gpa)** & **Degree** \\ \hline
1 & 5.74 & 0.325 & 10 & 6.93 & 0.532 \\
2 & 5.83 & 0.389 & 11 & 7.25 & 0.555 \\
3 & 5.89 & 0.365 & 12 & 7.54 & 0.611 \\
4 & 5.9 & 0.325 & 13 & 7.7 & 0.619 \\
5 & 5.95 & 0.405 & 14 & 8.03 & 0.611 \\
6 & 6.12 & 0.365 & 15 & 8.61 & 0.635 \\
7 & 6.7 & 0.421 & 16 & 8.86 & 0.651 \\
8 & 6.75 & 0.492 & 17 & 9.32 & 0.595 \\
9 & 6.85 & 0.476 & 18 & 9.47 & 0.643 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The relationship between collision pressure and reaction degree of PTFE/Al [15]. 4. The time step was set to 1 ms, and the reaction degree and temperature of the PTFE/Al reactive material at the next moment were calculated through Equations (27) and (28). \[y_{2}=y_{1}+\alpha\times t\] (27) \[T_{2}=T_{1}+\frac{\alpha\times Q}{C_{p}}-\Delta T\] (28)
5.