The application of temperature-modulated DSC to the glass transition region: II. Effect of a distribution of relaxation times

Abstract

An analysis of temperature-modulated differential scanning calorimetry (TMDSC) in the glass transition region is presented. It extends an earlier and simpler model by introducing a distribution of relaxation times, characterised by a Kohlrausch–Williams–Watts (KWW) stretched exponential parameter β, in addition to the usual kinetic parameters of relaxation, namely the Tool–Narayanaswamy–Moynihan (TNM) non-linearity parameter x and the apparent activation energy Δ h ∗. The present model describes, more realistically than did its predecessor, all the characteristic features of TMDSC in the glass transition region, and it has been used to examine the effects of the important experimental variables, namely the period of modulation and the underlying cooling rate. It is shown that, for typical experimental conditions in practice, it is likely that there well be an interaction between the vitrification process, due to the underlying cooling rate, and the dynamic glass transition whereby the complex heat capacity C p ∗ shows a sigmoidal decrease in a temperature range dependent on the modulation frequency. Accordingly, care must be exercised in the quantitative evaluation of TMDSC data in the glass transition region, and suggestions are made regarding the optimum procedures in this respect. Also, by comparing the cooling rate and modulation period required to define the same transition temperature for conventional DSC and C p ∗ , respectively, a correspondence between them is obtained which allows the magnitude of temperature fluctuations in Donth’s fluctuation dissipation theorem to be evaluated. Finally, it is shown that β and x have similar effects on conventional DSC cooling curves, but have very different effects on C p ∗ , whereby there is little effect of x but a significant broadening of the transition as β decreases. It is argued that the breadth of the C p ∗ transition therefore provides a measurement of β independent of the value of x, thus resolving a problem that has existed for some years.