# A Review of Degradation and Life Prediction of Polyethylene
## 5 Prediction Techniques for Polyethylene Materials
### Arrhenius Equation  
#### 5.2.1 General Arrhenius Equation  
Accelerated aging experiments offer a reliable foundation for estimating the life of polyethylene materials. Temperature influences the time to failure or aging efficiency of polyethylene materials, and both factors are important for more accurately estimating the performance of polyethylene materials. The Arrhenius connection is the foundation of the most significant method for polyethylene aging. [PERSON], a Swedish chemist, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Kinetic Model** & **Symbol** & **f(\(\alpha\))** \\ \hline \multicolumn{3}{c}{n-order reactions} \\ \hline First order & \(F_{1}\) & \(1-\alpha\) \\ Second order & \(F_{2}\) & \((1-\alpha)^{2}\) \\ \(\mathbf{n}^{th}\) order & \(F_{n}\) & \((1-\alpha)^{n}\) \\ \hline Diffusion & & \\
1-D diffusion & \(D_{1}\) & \(1/2\alpha\) \\
2-D diffusion & \(D_{2}\) & \([-\ln(1-\alpha)]^{-1}\) \\
3-D diffusion–Jander & \(D_{3}\) & \(3/2(1-\alpha)^{\frac{1}{3}}\left[1-(1-\alpha)^{\frac{1}{3}}\right]\) \\
3-D diffusion–Ginstling–Brownshtein & \(D_{4}\) & \(3/2\left[(1-\alpha)^{-\frac{1}{3}}-1\right]^{-1}\) \\ \hline Phase-boundary reactions & & \\ \hline Contracting area & \(R_{2}\) & \(2(1-\alpha)^{\frac{1}{2}}\) \\ Contracting volume & \(R_{3}\) & \(3(1-\alpha)^{\frac{1}{3}}\) \\ Prout–Tompkins & \(B_{1}\) & \(\alpha(1-\alpha)\) \\ expandedProut–Tompkins & \(B_{n}\) & \((1-\alpha)^{n}\mathbf{x}^{m}\) \\ First order withautocatalysis & \(C_{1}\) & \((1-\alpha)^{(1+KatX)}\) \\ \(\mathbf{n}^{th}\) order withautocatalysis & \(C_{n}\) & \((1-\alpha)^{n(1+KatX)}\) \\ \hline Nucleation and nuclei growth & & \\ \hline Avrami–Erofeev & \(A_{2}\) & \(2(1-\alpha)\)\([-\ln(1-\alpha)]^{\frac{1}{3}}\) \\ [PERSON]–[PERSON] & \(A_{3}\) & \(3(1-\alpha)\)\([-\ln(1-\alpha)]^{\frac{1}{3}}\) \\ [PERSON]–[PERSON] & \(A_{n}\) & \(n(1-\alpha)\)\([-\ln(1-\alpha)]^{\frac{1}{3\alpha}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Kinetic model and its conversion function [100]. presented the Arrhenius equation (Equation (14)) in 1889. It is an empirical chemical kinetic equation that describes the rate of reaction as a function of temperature [103]. The dependence of the kinetics of some simple chemicals' chemical reactions on the critical element of temperature is extremely well described by the Arrhenius equation. The material produces a very modest reaction rate at very low temperatures, according to the Arrhenius equation, yet the minimum value will not be zero. The following conditions must be met to use the Arrhenius equation: (1) There must be only one main chemical reaction that causes thermal deterioration within a specific temperature range, and this significant chemical reaction should serve as the test's starting point [104; 105; 106; 107]. (2) First-order or other fixed-order kinetics govern the process of degradation [105; 108]. (3) The degradation does not appreciably alter at time zero. (4) There has been no phase change [106; 107]. (5) The experimental study's temperature range was somewhat constrained to prevent the accuracy of the test results from being impacted by further degradation mechanisms [109]. (6) Throughout the test's deterioration range, the activation energy should remain constant [110]. The non-exponential form of Equation (16) can be used to represent the Arrhenius equation, making it simpler to use and allowing for graphical interpretation [111]:  
\[\ln K(T)=\ln A-\frac{E_{a}}{RT} \tag{16}\]  
However, it is not accurate enough to detect the aging process of the material with a single experiment, so it is necessary to learn more about the change curve of material properties versus time under several experimental conditions, as shown in Figure 3, and use it as a foundation for material life speculation. By plotting the relationship between \(lnK(T)\) and \(1/T\) in the equation's linear relationship, the least squares method can be used to best fit the data.