# The Unique Model-Based Analysis

## Model-Based Kinetics for Comprehensive Analysis of Chemical Reactions

The extraordinary model-based analysis was developed by NETZSCH. It uses powerful cutting-edge mathematical calculations to create the best kinetic model; the different kinetic models can then also be compared statistically. Therefore, this approach has none of the disadvantages which can be observed when using model-free methods.

### The Model-Based Kinetic Analysis Is Based on Three Assumptions:

**1. **The reaction consists of several elementary reaction steps, and the reaction rate of each step can be described by a kinetic equation of its own for the given step, depending on the concentration of the initial reactant e_{j}, the concentration of product p_{j}, the pre-exponential factor A_{j} and the activation energy E_{j}, speciﬁc only for this step with number j, as follows: _{}^{}

Each step has its own reaction type described by the function f_{j} (e_{j};p_{j}).

Some examples of these functions include a second-order reaction which has f = e^{2}, a Prout–Thompkins reaction with acceleration which has f = e^{m}p^{n} and a reaction with a one-dimensional diffusion which has f = 0.5/p. The number of kinetic equations is equal to the number of reaction steps; the concentration for each reactant increases for the reaction steps where this reactant is a product, and decreases for the reaction steps where this reactant is a starting substance.

**2.** All kinetic parameters including the activation energy, pre-exponential factor, order of reaction, and reaction type are assumed to be constant during the reaction progress for every individual reaction step.

**3.** The total thermoanalytical signal is the sum of the signals of the individual reaction steps. The signal of each step is calculated as the reaction rate multiplied by the total effect of the given step; e.g., total enthalpy change or total mass loss.

Model-based kinetic analysis offers the possibility of visual design for kinetic models with an **unlimited **number of steps connecting in **any **combinations.

The models can be flexibly designed by adding new reactions as independent, consecutive or competitive steps to **any **place in the model.

A simulated reaction step can be visually moved to the corresponding step on the experimental curve. Then the parameters of this step can be optimized.

## Model-Based Methods’ Results

Approximately 95% of all chemical reactions are multi-step reactions. This requires a multi-step analytical engine as offered by the *Kinetics NEO *software.

The engine uses non-linear regression methods and allows for the optimization of parameters for individual steps or for the complete model. The fit results present the agreement between the experimental and simulated curves for:

- Signal
- Conversion
- Conversion rate
- Concentration of all reactants
- Reaction rates for all steps