Temperature modulated differential scanning calorimetry : modelling and applications
The research described in this thesis focused on the TMDSC technique with respect to both theoretical problems and applications. Theoretically, modelling work has been performed to address the effects of heat transfer in the measuring cell on both dynamic and quasi-isothermal TMDSC experiments. The problems of heat transfer generally influence the measured complex heat capacity and phase angle values, but eventually affect the precise measurements of other frequency dependent quantities such as the in-phase and out-of-phase heat capacities. A procedure has been suggested to correct the measured phase angle obtained by dynamic TMDSC using the scaled complex heat capacity trace (Chapter 3). The modulation frequency dependence of the instrumental phase angle has been fully investigated using more realistic models in terms of various heat transfer interface qualities, sample properties and sensor properties. In these models, it is emphasised that the measured temperatures are the sensor temperatures rather than the sample temperatures, thus, the contributions of the sensor's properties to the heat transfer are, for the first time, separated from the overall effects (Chapter 4 and Chapter 5). The consequent effects of heat transfer on the sample's heat capacity measurements are investigated based on the models suggested (Chapter 6). All the modelling results are compared with the corresponding experimental data obtained by ADSC (Mettler-Toledo Ltd) and they are in good agreement. Ripples and fluctuations which appear on the experimental signals during the glass transition and cold crystallisation transition have been simulated using* a simple model in which the period of the modulation signals changes with the time during the transitions, and then, been shown to be artefacts of the Fourier transformation process used by TMDSC evaluations (Chapter 7). The applications of TMDSC to both research and commercial samples are reported in terms of differing either the experimental conditions or the thermal history of the sample. Separating of time dependent kinetic processes from the time independent dynamic processes has been applied on the studies of the glass transition (for polycarbonate and poly(ethylene terephthalate)), the cold crystallisation (for poly(ethylene terephthalate)), the melting transition (for poly(ethylene terephthalate) and lead/tin alloys), the clearing transition of a liquid crystal polymer, and the vitrification of an epoxy resin under quasi-isothermal conditions. The main conclusion drawn from these studies is that the in-phase heat capacity is greatly influenced by the frequency of the temperature modulations even when the underlying heating (or cooling) rate remains the same. This strongly implies that the sample undergoes different structural change under different modulation conditions for the melting transition and clearing transition, but not for the glass transition and cold crystallisation. However, the interpretations of the in-phase heat capacity and out-of- phase heat capacity still need to be clarified. The detection of the glass transition and clearing point for the liquid crystal polymers, and the determination of wax appearance temperature for crude oils, show the ability of TMDSC for combining the sensitivity of a measurement at high instantaneous heating or cooling rates with the resolution obtained by measuring at a low underlying heating or cooling rates. The work on the isothermal curing of the epoxy resins displays the ability of TMDSC on measuring the heat capacity of the sample and its variation under the quasi-isothermal conditions. The frequency dependent complex heat capacity during the glass transition provides a window to measure the apparent activation energy of the transition, which is different, in some extent, from the window used by conventional DSC. The results are correlated by a shift factor. Some shortcomings of TMDSC, however, have been noticed in both modelling and application work. Firstly, any experiments for the purpose of either understanding or the quantitative measurements of TMDSC output quantities should be performed under carefully selected conditions which can satisfy the linear response assumption. Secondly, some signals in particular those associated with kinetic processes may not be fully sampled by TMDSC due to the limit of the observing window of a modulation. Thirdly, when the sensitivity is improved on TMDSC by separating the kinetics processes and noises from the dynamic processes, the TMDSC evaluation procedure introduces mathematical artefacts into the output signals. As a consequence, it is preferable to include as many temperature modulations as possible within any transition being studied in order to obtain good quality experimental signals by eliminating or minimising these artefacts, which, however, is not an easy task for some very abrupt transitions such as melting of metals.