DIFFERENTIAL SCANNING CALORIMETRY

Whenever a chemical reaction takes place heat is either absorbed or liberated. Often times a chemical raction can usually be initiated by raising the temeprature of the system. A differential scanning calorimeter (DSC) measures the differential heat flow required to maintain a sample of a material and an inert reference at the same temperature. The temperature is usually programmed to scan over a temperature range at a preddetermined rate. Therefore the change in enthalpy associated for a given reaction can be easily obtained from heat flow data. DSC also provides an opportunity for measuring the rate of reaction. This type of analysis can reveal information about the kinetic parameters and mechanisms of the process.

This method incorporates a single DSC scanning run (Borchardt, 1956). The partial areas under the single thermogram are utilized to transform the experimental data into degree of conversion and the rate of heat evolution to determine the instantaneous reaction rates. The reaction order, activation energy and frequency factor are determined from the relationship between the reaction rate, conversion and temeprature using the log of the kinetic equation and least square multiple linear regression of the data. The approach is outlined below in figure one:

The advantage of this method is that it requires only a single DSC scan. The method however is only applicable to nth order decompositions. Complex decomposition mechanisms cannot be identified and therefore kinetic parameters obtained are incorrect.

This method (Ozawa, 1970) utilizes the relationship between the peak temperature of the reaction exotherms and the heating rates to determine reaction kinetic parameters. Verification of the kinetic parameters is obtained using an isothermal test. Similar aged and unaged samples are run and their respective reaction peaks recorded. If on an equal weight basis the peak area or displacement from baseline of the aged sample is found to be one half that of the unaged sample then the reactions kinetics are confirmed for the temperature range explored. The disadvantage of this method is that it is also based on the first order kinetic equation. Therefore it cannot be applied to complex decomposition reactions (i.e. autocatalytic reactions).

This method (Duswalt, 1968) measure the extent of reaction directly as a function of temperature and time. Several separate samples are held in the calorimeter at a given temeprature but for varying lengths of time. They are then programmed through their decompositions. The decrease in the exothermic peak area per unit sample wight as a functin of the previous isothermal exposure time is a measure of reaction rate at the set temperature. Rate constants at all experimental temperatures are calculated and used for activation energy and frequency factor calculations using the Arrhenius equation. The use of this method as presented in past literature oversimplifies the autocatlytic decomposition mechanism. Predictions at lower temperatures of decomposition can be poor.

Recent studies in kinetic parameter estimation from DSC analsysis suggest modifications to the above procedures to improve the accuracy and applicability of the decomposition equations.

The rate of decomposition reaction is generally a function of the reactant concentrations and temperature. The former determines the reaction mechanism and the latter is established from the Arrhenius equation. In isothermal studies the temperature variable can be eleminated and data can therefore be interpreted in a simpler manner. The advantage is that more reliable kinetic data can be obtained with a wider range of applicability.

During isothermal experiments two patterns of behavior are usually observed. The maximum reaction rate occurs at the very beginning and slowly decreases until reaction completion. This is the mark of an nth order reaction. Otherwise the reaction rate at the beginning is slow and is followed by a rising rate that continues through a maximum sometime during the experiment. This is the mark of an autocatalytic reaction.

1. Borchardt, H.J., Daniels, F., J. Am Chem. Soc., vol 79, 1956, p. 41
2. Duswalt, A.A., Proc. Amer. Chem. Soc. Symp. Analytical Calorimetry, 1968, p. 313
3. Ozawa, T., J. Thermal. Anal., Vol. 2, p. 301 (1970).