# Effect of LNR-g-MMA on the Mechanical Properties and Lifetime Estimation of PLA/PP Blends
## 2 Experimental
### Kinetic Analysis  
Determination of the kinetic parameters of thermal degradation can be calculated with data obtained from the TGA analysis. In general, these parameters were evaluated by amodel\(-\)free kinetic method. The rate of reaction (dw/dt) for thermal degradation can be calculated as follows:  
\[\frac{\mathrm{dw}}{\mathrm{dt}}\quad=\quad\mathrm{k}(\mathrm{T})\cdot\mathrm{f}( \mathrm{w}) \tag{3}\]  
where k(T) is the reaction rate constant, w is the conversion degree during the degradation reaction, f(w) is the reaction model, and T is the absolute temperature (K). The Arrhenius equation can describe the temperature dependence of the rate constant. \[\mathrm{k}(\mathrm{T})\quad=\quad\mathrm{A}\cdot\exp\big{(}-\frac{\mathrm{E _{a}}}{\mathrm{RT}}\big{)} \tag{4}\]  
where A is the pre\(-\)exponential factor, \(\mathrm{E_{a}}\) is the activation energy, and R is the gas constant (8.314 J/mol \(\cdot\) K). For non-isothermal TGA, the conversion degree (w) can be determined as the ratio of the actual weight loss at time (t) to the total weight loss corresponding to the decomposition process. \[\mathrm{w}(-)\quad=\quad\frac{\mathrm{w_{i}}-\mathrm{w_{t}}}{\mathrm{w_{i}}- \mathrm{w_{f}}} \tag{5}\]  
where \(\mathrm{w_{i}}\), \(\mathrm{w_{t}}\) and \(\mathrm{w_{f}}\) are the actual weight of the sample at the initial weight, weight at time (t), and final weight of a sample, respectively. By combining Equations (3) and (4), the following Equation (6) can be obtained:  
\[\frac{\mathrm{dw}}{\mathrm{dt}}\quad=\quad\mathrm{A}\cdot\exp\big{(}-\frac{ \mathrm{E_{a}}}{\mathrm{RT}}\big{)}\cdot\mathrm{f}(\mathrm{w}) \tag{6}\]  
For non-isothermal conditions, in which the samples are at a heating rate (\(\beta=\mathrm{dT}/\mathrm{dt}\)):  
\[\frac{\mathrm{dw}}{\mathrm{dt}}\quad=\quad\frac{\mathrm{dw}}{\mathrm{dT}} \times\frac{\mathrm{dT}}{\mathrm{dt}}\quad=\quad\beta\frac{\mathrm{dw}}{ \mathrm{dT}} \tag{7}\]  
The rate of degradation (dw/dt) equal to \(\beta\)(dw/dT) is arranged and modified as follows:  
\[\frac{\mathrm{dw}}{\mathrm{dT}}\quad=\quad\frac{\mathrm{A}}{\beta}\cdot\exp \big{(}-\frac{\mathrm{E_{a}}}{\mathrm{RT}}\big{)}\cdot\mathrm{f}(\mathrm{w}) \tag{8}\]  
Following this rearrangement, Equation (9) is the fundamental form of kinetic analytical methods, which is used to evaluate the kinetic parameters for the thermal degradation data. One of the most popular methods is the Kissinger-Akahira-Sunose (KAS) method, which is the isoconversical model\(-\)free kinetic method with multiple heating rates. It is generally known that the KAS method can be used to evaluate the activation energy (\(\mathrm{E_{a}}\)). \[\ln\frac{\beta}{\mathrm{T}^{2}}\quad=\quad\mathrm{constant}-\frac{\mathrm{E_{ a}}}{\mathrm{RT}} \tag{9}\]  
The same degree of conversion exists at different heating rates. Thus, the activation energy can be calculated from the slope of a linear plot of \(\ln\) (\(\beta\)/T\({}^{2}\)) against 1000/T at the constant conversion degree (w). The kinetic analysis of the non-isothermal data was obtained by the KAS method. It is well known that activation energy can be used to predict the lifetime of materials. Using the \(\mathrm{E_{a}}\) obtained for a conversion degree of 0.05, the material lifetime (\(\mathrm{t_{T}}\)) was calculated by analyzing the lifetime of rubber at various operating temperatures (\(\mathrm{T_{T}}\)). This conversion degree value might cause a substantial drop in the mechanical properties of a material.