THERMOKINETICS Sparse Data Software (TKsd)

Evaluation of Kinetic Parameters from Sparse,
Discontinuously Collected Thermoanalytical Data

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Thermokinetics Sparse Data Software (TKsd) based on advanced kinetic and statistical model selection approaches (AIC&BIC)

TKsd Software allows among others :

  • Life-time prediction from small amount of experimental points
  • Determination of the prediction bands
  • Simulation of the reaction course under any temperature mode
  • Verification of the predictions by additional experimental data

DATA COLLECTION AND IMPORTATION

Kinetic analysis

Evaluation of kinetic models and parameters

Ranking of kinetic models according to statistical criteria AIC & BIC

Prediction of the reaction course at different temperature modes using best ranked kinetic model

Predictions

Isothermal temperature mode, Time-Temperature-Transformation (TTT) diagram

Step-wise temperature mode

Modulated temperature mode

Worldwide real atmospheric temperature profiles

STANAG climatic categories

User customized temperature mode

Mixed temperature modes

Kinetic analysis based on noisy sparse data

Determination of prediction bands (e.g. 95% confidence) and verification of the predictions

Prediction of the change of material properties with the prediction bands at different temperature modes

Thermokinetics Sparse Data Software (TKsd) based on advanced kinetic and statistical model selection approaches (AIC&BIC)

TKsd Software allows among others :

  • Life-time prediction from small amount of experimental points
  • Determination of the prediction bands
  • Simulation of the reaction course under any temperature mode
  • Verification of the predictions by additional experimental data

DATA COLLECTION AND IMPORTATION

Kinetic analysis

Evaluation of kinetic models and parameters

Ranking of kinetic models according to statistical criteria AIC & BIC

Predictions

Isothermal temperature mode, Time-Temperature-Transformation (TTT) diagram

Step-wise temperature mode

Modulated temperature mode

Worldwide real atmospheric temperature profiles

STANAG climatic categories

User customized temperature mode

Mixed temperature modes

Kinetic analysis based on noisy sparse data

Determination of prediction bands (e.g. 95% confidence) and verification of the predictions

Prediction of the change of material properties with the prediction bands at different temperature modes

Thermokinetics Sparse Data Software (TKsd) based on advanced kinetic and statistical model selection approaches (AIC&BIC)

TKsd Software allows among others :

  • Life-time prediction from small amount of experimental points
  • Determination of the prediction bands
  • Simulation of the reaction course under any temperature mode
  • Verification of the predictions by additional experimental data

DATA COLLECTION AND IMPORTATION

Kinetic analysis

Evaluation of kinetic models and parameters

Ranking of kinetic models according to statistical criteria AIC & BIC

Predictions

Isothermal temperature mode, Time-Temperature-Transformation (TTT) diagram

Step-wise temperature mode

Modulated temperature mode

Worldwide real atmospheric temperature profiles

STANAG climatic categories

User customized temperature mode

Mixed temperature modes

Kinetic analysis based on noisy sparse data

Determination of prediction bands (e.g. 95% confidence) and verification of the predictions

Prediction of the change of material properties with the prediction bands at randomized temperature fluctuations

Data collection and importation

At least 20-30 experimental points have to be collected at a minimum three temperatures. Additional experiments at different temperatures or additional time-points increase the accuracy of the kinetic analysis. In our case study the experiments used for kinetic analysis were performed at 45, 37, 25 and 5°C.

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The user can import any data in ASCII-format (.txt-files) independent of its source containing information about:

  • Time
  • Temperature
  • Measured quantity changing as a function of time and/or temperature and/or relative humidity as e.g. the sample mass, heat flow, concentration of active component, amount of degradation product etc.
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Kinetic analysis

Fig. 1 – Choose the “Kinetics” tool; data collected at 45, 37, 25 and 5°C will be used in the kinetic analysis.

Evaluation of kinetic models and parameters

Fig. 1– Evaluation of Kinetic Models and parameters. In this example: (i) For the best model selection (‘1 step & 2 steps’) the Automatic mode is chosen (ii) The ‘y-init’-value is checked, therefore it will be optimized during calculations. (iii) The y-end value is unchecked and set to zero, therefore during calculations the final y-end value is forced to be zero. (iv) All data are considered in the kinetic analysis.

Best model selection:

For the best model selection one can choose between the Automatic (recommended) or the Custom mode which is more advanced and requires manual introduction of the kinetic equations.

User can choose between:

  • ‘1 step’ (for one-stage reaction)

or

  • ‘1 step & 2 steps’ (for two-stages reaction)

Successive models are consecutively checked to find the best fit of the experimental data. During fitting procedure all kinetic models present in the software library (for one- and two-stages reactions) are considered.

 

Input of ‘Initial’ and ‘End’ values (‘y-init’ and ‘y-end’):

The ‘Initial’ and ‘End’ values are generally picked up from the experimental data points however the user has the possibility to fix or optimize these values during calculations.

  • If the box is checked, the y-init, y-end or both values are optimized during calculations.
  • If the box remains unchecked, y-init, y-end or both values are forced to the entered values accordingly.


Experimental data:

During the determination of the best kinetic model one can change the range of data used in the kinetic analysis – see the red-marked top-right rectangle

Ranking of kinetic models according to statistical criteria AIC & BIC

The selection of the best kinetic models describing the reaction course is based on Akaike and Bayesian Information criteria (AIC&BIC). The application of both criteria helps balance between the goodness of the fit of the experimental results by the prediction curves, the number of required models and the number of parameters used.

  • During selection of the best model not only the quality of fit (such as the sum of residual squares), but also the number of data points and model parameters are considered.
  • Applied procedure indicates not only which model is more likely to be correct but also quantifies how much more likely by application of the AIC and BIC weights ‘w’.
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The parameters of the best kinetic models can be additionally optimized after selection of the tool « Optimization ».

The software has already chosen which model is the best, but one can additionally select the other models (0-th order in Fig.3 and 1-st order in Fig.4) for comparison.

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Predictions

For the prediction of the reaction course at any temperature profile click the icon “Prediction”.

Isothermal temperature mode, Time-Temperature-Transformation (TTT) diagram

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TKsd Software allows the determination of Temperature-Time-Transformation (TTT) diagram which displays the equivalent time temperature points for which the arbitrarily chosen reaction progress is the same.

TTT plot can be used to determine immediately the time at which the required reaction extent is reached at chosen temperature.

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Step-wise temperature mode

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Modulated temperature mode

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Worldwide real atmospheric temperature profiles

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STANAG climatic categories

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User customized temperature mode

Fig. 1 – The user can predict the material properties at any customized temperature profile which
has to be introduced in ASCII-format (.txt-files). The screen shows the importation of the customized profile.

The influence of the temperature fluctuations on the reaction course can be evaluated for any customized temperature profiles recorded by e.g. commonly applied data loggers that collect the temperature and humidity during a chosen period.

Fig. 2 – The change of the material properties at temperature profile recorded
by data logger: the value of 15% corresponding to the acceptable limit (8.1 a.u.)
is not reached after ca. 8 months.

Mixed temperature modes

Fig. 1 – The “Mixed”-function allows to combine consecutively the different
temperature conditions. This example displays the prediction of the decomposition
course the following temperatures: recorded by the data logger, isothermal (5°C,
characteristic for the cold chain) and daily climate fluctuations.
The value of 15% corresponding to the acceptable limit (8.1 a.u.) is reached
after 13.7 months at these temperature fluctuations.

Kinetic analysis based on noisy sparse data

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Determination of prediction bands (e.g. 95% confidence) and verification of the predictions

The prediction bands are determined by the bootstrap method which is based on Monte Carlo approach frequently used in applied statistics. For the statistical analysis one can choose between resampling the residuals or data points.

Fig. 1 – Determination of prediction bands (95% confidence). For the statistical analysis one can apply the residuals or the data points.

The plots below show the prediction of the reaction course at 5°C based on the best kinetic model evaluated from the data collected at 45, 37, 25 and 5°C (filled circles). The data points collected after 180 days serve for the verification of the predictions. The dashed lines depict the prediction bands with 95% confidence.

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Prediction of the change of material properties with the prediction bands at randomized temperature fluctuations

AKTS Thermokinetics Sparse Data software (TK-sd) allows simulation of the stability of the materials and their degree of degradation under any temperature conditions occurring during their storage and transport before the final use. The software evaluates by the bootstrap method the prediction bands with 95% confidence (dashed lines in the plot).

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