The Non-Parametric Kinetics method page

INDEX

PRESENTATION

The NON-PARAMETRIC KINETICS (NPK) 1,2 is a recently developed method for the kinetic treatment of thermoanalytical data. This method introduces a new point of view in kinetic analysis. As all the classical methods it is based on the presumption of the validity of the following equation:

[1]

NPK regards the reaction rate as a surface in a three dimensional space where the axis are the temperature ,the degree of conversion and the rate of change of the degree of conversion. This surface, which is continuous, can be discretised and organised as an n´ m matrix, where the columns account for the temperature, from T1 to Tm, while the rows refer to different degrees of conversion, from a1 to an, as can be shown in Equation. 2:






[2]




Matrix A can be expressed as the product of two column vectors:

[3]

[4]

[5]

where vector u contains all the information about the kinetic model and vector v about the function f(T).

It is possible to evaluate the reaction rate using only the vectors u and v, because any value of the reaction rate can be expressed as , where g(a) and f(T) are obtained by interpolation of the elements of u and v at the required values of degree of conversion and temperature.

Even though the kinetic parameters, such as activation energy, frequency factor or reaction order, are not necessary to reproduce the system behaviour or to simulate it in different conditions, it is also possible to use the results of the NPK method to obtain model parameters from vector u and the activation energy and the frequency factor from vector v.

Therefore, applying a procedure that is able to decompose matrix A into two vectors as expressed in Equation 3, the vectors u and v will be obtained and so the reaction kinetics. The NPK method performs this decouplement using the Singular Values Decomposition (SVD) 3.

It is worth mentioning that the development of the NPK method does not have any limitation in the source of the data, it can be provided by any TA technique that gives reaction rate information as a function of temperature and degree of conversion, for example, Differential Scanning Calorimetry or Thermogravimetry, but also another technique which is not commonly used for kinetic analysis: Adiabatic Calorimetry.

The NPK method has been already tested using data from DSC and TGA 1,2, Reaction Calorimetry and Adiabatic Calorimetry 4, all of them experimental and simulated in order to obtain kinetic information.

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REFERENCES

  1. R. Serra, J. Sempere and R. Nomen, Therm. Acta, 316, 1998

  2. R. Serra, R. Nomen and J. Sempere, J. Thermal Anal., 52, 1998

  3. G.H. Golub and C.F. Van Loan, Matrix Computation; The Johns Hopkinns University Press, 1989

  4. J. Sempere, R. Nomen and R. Serra, J. Thermal Anal., in press

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