2.4.1. Coats–Redfern (CR) Method

The ordinary differential equation in Equation (3) can be handled by integration by separation of the variable to obtain a temperature integral function as shown in Equation (4). However, an analytical solution is not attainable.

$$\lg(\theta) = \int\_0^{\theta} \frac{d\theta}{f(\theta)} = \int\_{T\_0}^T \frac{A}{\beta} \exp^{(-\frac{F}{RT})} \, dT \tag{4}$$

Note that *g*(*θ*) represents an integral decomposition model that represents the reaction mechanism that relates to the solid-state degradation. A couple of such models are given in Table 2. The logarithmic transformation of Equation (3) alongside Equation (4) yields the CR model for the derivation of the kinetic parameters, as shown in Equation (5):

$$\ln\left(\frac{g(\theta)}{T^2}\right) = \ln\frac{AR}{\beta E}\left(1 - 2\frac{RT}{E}\right) - \frac{E}{RT} \tag{5}$$

**Table 2.** Empirical correlations for *g*(*θ*) on different reaction mechanisms [28,29].


The plot of the left-hand side of Equation (5) against the reciprocal of temperature yields, approximately, a linear curve from whose slope the activation energy can be obtained. It is assumed that *RT <sup>E</sup>*; therefore, the intercept is given as *intercept* <sup>=</sup> ln *AR <sup>β</sup><sup>E</sup>* , from which the pre-frequency factor is computed.

## 2.4.2. Differential Friedman Method (DFM)

If the natural logarithm is applied to Equation (3), it yields Equation (6), which is commonly referred to as the differential Friedman's kinetic model.

$$\ln\left[\frac{d\theta}{dt}\right] = \ln\left[\beta\left(\frac{d\theta}{dT}\right)\right] = \ln[Af(\theta)] - \frac{E}{RT} \tag{6}$$

In Friedman's relation, the conversion function, *f*(*θ*), is assumed constant. This implies that the solid-state degradation is primarily dependent on the mass-loss rate and is independent of the temperature. The linear plot of ln *dθ dt* against <sup>1</sup> *<sup>T</sup>* is generated for different heating rates, and the activation energy is determined from the slope *slope* <sup>=</sup> <sup>−</sup> *<sup>E</sup> R* . It is important to note that the use of the derivative conversion data makes the DFM prone to noise sensitivity and numerical instability, and therefore, caution must be exercised in the data interpretation [36].
