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Modulated differential scanning calorimetry in the glass transition region

VI. Model calculations based on poly(ethylene terephthalate)

Journal of Thermal Analysis and Calorimetry
Authors: B. Wunderlich and I. Okazaki

Abstract  

Temperature-modulated calorimetry (TMC) allows the experimental evaluation of the kinetic parameters of the glass transition from quasi-isothermal experiments. In this paper, model calculations based on experimental data are presented for the total and reversing apparent heat capacities on heating and cooling through the glass transition region as a function of heating rate and modulation frequency for the modulated differential scanning calorimeter (MDSC). Amorphous poly(ethylene terephthalate) (PET) is used as the example polymer and a simple first-order kinetics is fitted to the data. The total heat flow carries the hysteresis information (enthalpy relaxation, thermal history) and indications of changes in modulation frequency due to the glass transition. The reversing heat flow permits the assessment of the first and higher harmonics of the apparent heat capacities. The computations are carried out by numerical integrations with up to 5000 steps. Comparisons of the calculations with experiments are possible. As one moves further from equilibrium, i.e. the liquid state, cooperative kinetics must be used to match model and experiment.

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Modulated differential scanning calorimetry in the glass transition region

II. The mathematical treatment of the kinetics of the glass transition

Journal of Thermal Analysis and Calorimetry
Authors: B. Wunderlich, A. Boller, I. Okazaki, and S. Kreitmeier

Temperature-modulated differential scanning calorimetry (TMDSC) is based on heat flow and represents a linear system for the measurement of heat capacity. As long as the measurements are carried out close to steady state and only a negligible temperature gradient exists within the sample, quantitative data can be gathered as a function of modulation frequency. Applied to the glass transition, such measurements permit the determination the kinetic parameters of the material. Based on either the hole theory of liquids or irreversible thermodynamics, the necessary equations are derived to describe the apparent heat capacity as a function of frequency.

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Abstract  

The quality of measurement of heat capacity by differential scanning calorimetry (DSC) is based on the symmetry of the twin calorimeters. This symmetry is of particular importance for the temperature-modulated DSC (TMDSC) since positive and negative deviations from symmetry cannot be distinguished in the most popular analysis methods. Three different DSC instruments capable of modulation have been calibrated for asymmetry using standard non-modulated measurements and a simple method is described that avoids potentially large errors when using the reversing heat capacity as the measured quantity. It consists of overcompensating the temperature-dependent asymmetry by increasing the mass of the sample pan.

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