Kinetic Analysis, Model Validation & Thermal Safety

Method Overview

This tool performs a complete, three-stage analysis based on a single DSC curve of an exothermic reaction.

Step 1: Kinetic Fit with Borchardt & Daniels Method

The first step is to determine the fundamental kinetic parameters of the reaction. The Borchardt & Daniels method is a model-fitting technique that assumes:

• An n-th order reaction kinetic, where the reaction model is $f(\alpha) = (1-\alpha)^n$.
• The validity of the Arrhenius Law, $k(T) = A \cdot e^{-E_a / (RT)}$.

By combining these assumptions, the working equation is obtained and linearized to allow for a linear regression:

$$ \ln\left( \frac{d\alpha/dt}{(1-\alpha)^n} \right) = \ln(A) - \frac{E_a}{R} \cdot \frac{1}{T} $$

The algorithm tests different values of the reaction order $n$ and selects the one that maximizes the correlation coefficient ($R^2$), thus providing the "kinetic triplet": $E_a$ (Activation Energy), $A$ (Pre-exponential Factor), and $n$.

Step 2: Kinetic Model Validation

A model is only useful if it represents reality well. To validate the found parameters, the tool solves the fundamental differential equation of kinetics ($\beta \frac{d\alpha}{dT} = A e^{-E_a/RT}(1-\alpha)^n$) to generate a theoretical DSC curve. This curve is then superimposed on the experimental one, allowing for an immediate visual assessment of the model's quality.

Step 3: Thermal Safety Assessment (Isothermal Td24)

Using the validated kinetic parameters, an isothermal simulation is performed. The tool calculates the **Td24**, defined as the constant temperature at which the material takes **24 hours to reach 5% conversion**. This is a conservative safety parameter useful for defining safe long-term storage conditions.