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Abstract  

The response of temperature-modulated differential scanning calorimetry (TMDSC) to irreversible crystallization of linear polymers was investigated by model calculations and compared to a number of measurements. Four different exotherms were added to a typical modulated, reversible heat-flow rate in order to simulate irreversible crystallization. It was found that the reversing heat-flow rate of the TMDSC in response to such irreversible crystallization exotherms is strongly affected by tbe shape of the transition and the phase-angle where the exotherm occurs. A comparison with the experimental data gave valuable insight into the transitions, as well as the nature of the TMDSC response which is usually limited to an analysis of the first harmonic term of the Fourier series that describes the heat-flow rate.

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The results from temperature modulated DSC in the glass transition region of amorphous and semicrystalline polymers are described with the linear response approach. The real and the imaginary part of the complex heat capacity are discussed. The findings are compared with those of dielectric spectroscopy. The frequency dependent glass transition temperature can be fitted with a VFT-equation. The transition frequencies are decreased by 0.5 to 1 orders of magnitude compared to dielectric measurements. Cooling rates from standard DSC are transformed into frequencies. The glass transition temperatures are also approximated by the VFT-fit from the temperature modulated measurements. The differences in the shape of the curves from amorphous and semicrystalline samples are discussed.

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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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Abstract  

In a temperature-modulated calorimetric method using the same apparatus as a standard differential scanning calorimeter, we have to pay attention to the thermophysical parameters of the apparatus, which cause phase shift in ac temperatures, such as heat capacity of base plate, heat capacity of a pan, thermal conductance between a heater and base plate, and thermal conductance between a pan and base plate. We performed the analysis of the thermal system of the apparatus with these parameters. Beside the theoretical consideration, we carried out heat capacity measurement in a wide range of modulation periods. We found that the experimental results were well-expressed in terms of these thermophysical parameters.

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Abstract  

Contributions of modern, temperature-modulated calorimetry are qualitatively and quantitatively discussed. The limitations are summarized, and it is shown that their understanding leads to new advances in instrumentation and measurement. The new thermal analysis experiments allow to separate reversing from irreversible processes. This opens the irreversible states and transitions to a description in terms of equilibrium and irreversible thermodynamics. Amorphous systems can be treated frommacroscopic to nanometer sizes with weak to strong coupling between neighboring phases. Semicrystalline, macromolecular systems are understood on the basis of modulated calorimetry as globally metastable, micro-to-nanophase-separated systems with locally reversible transitions.

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Abstract  

Indium was analyzed with both, standard differential scanning calorimetry (DSC) and temperature-modulated DSC (TMDSC) using sinusoidal and saw-tooth modulation. Instrument and sample effects were separated during nucleated, reversible melting and crystallization transitions, and irreversible crystallization with supercooling. The changes in heat flow, time, and sample and reference temperatures were correlated as functions of heating rate, mass, and modulation parameters. The transitions involve three regions of steady state (an initial and a final region before and after melting/crystallization, a region while melting/crystallization is in progress) and one region of approach to steady state (melting peak to final steady state region). Analyses in the time domain show promise when instrument lags, known from DSC, are used for correction of TMDSC. A new method of integral analysis is introduced for quantitative analysis even when irreversible processes occur in addition to reversible transitions. The information was derived from heat-flux calorimeters with control at the heater block or at the reference temperature sensor.

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.1016/0040-6031(95)90466-2 . 9. Wunderlich , B , Okazaki , I , Ishikiriyama , K , Boller , A . Melting by temperature-modulated calorimetry . Thermochim Acta . 1998 ; 324 : 77 – 85 . 10.1016/S0040

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, Seferis , C 1998 J Therm Anal Calorim 54 : 501 – 519 10.1023/A:1010134307537 . 25. Androsch , R , Pyda , M , Wang , H , Wunderlich , B 2000 A study of temperature modulated

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. Energy Fuel . 16 : 470 – 476 10.1021/ef010233r . 45. Wunderlich , B , Okazaki , I , Ishikiriyama , K , Boller , A . 1998 . Melting by temperature-modulated calorimetry . Thermochim

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